BANSAL CLASSES TARGETIIT JEE 2007 XI (P, Q, R, S) ill
s
C O N T E N T S
KEY CONCEPTS EXERCISE-I EXERCISE -II EXERCISE-III ANSWER KEY
KEY
CONCEPTS
THINGS TO REMEMBER ds ; a = — dv = v — dv v= — — dt dt ds ; s = Jvdt; = Ja dt ; = Ja ds where the symbols have their usual meaning . The equations ofmotion for a body moving in straight line with uniform acceleration, are , 1 * = ut h——=•v t — — r - \(m) 2v - 2_L1 u + 2as (i) v = u + at (ii) s=|—r—11 ' v + u^ (iv) s = u + ^ a ( 2 n - l ) (v) v
2.
u + V
a t
t
a t
2
n
If a body is thrown vertically up with a velocity u in the uniform gravitational field then (neglecting air resistance): (i) Maximum height attained H= (ii) Time of ascent = time of descent = — g 2u (iii) Total time of flight (iv) Velocity of fall at the point of projection=u downwards :
KINEMATIC GRAPH: Slope ofthe displacement time graph at any particular time gives the magnitude ofthe instantaneous velocity at that particular time. Slope ofthe v -1 graph will give the magnitude of the instantaneous acceleration. The area between the v - t graph, the time axis and the ordinates erected at the beginning & end oftime interval considered will represent the total displacement of the body. 5. RELATIVE VELOCITY: (a) Velocity of 'A' relative to 'B' is given by V = V - V • V refers to the velocity which 'A' appears to have as seen by B. The above idea of 1 dimensional relative motion can be extended to motion in 2 dimensions. (b) Angular velocity of A relative to B i.e. co is given by velocityof ArelativetoBinadirectionperpendiculartoAB ®AB AB 6. LEVEL GROUND PROJECTILE MOTION: When abody is thrown obliquely (in a vertical plane) into the uniform gravitationalfieldthen the trajectory (actual path of motion) is a parabola. The horizontal component of velocity ucos a remains unchanged where as vertical component decreases up to the maximum height and then increases. (a) Time taken to reach the height point t ^ usina i y a (minimum (b) Maximum height H - u sm velocity) 2g AB
A
B
AB
AB
=
2
(c) Total time of flight
•
2
=2t
u cos a
H
(d) Horizontal range = (ucos a). T= - (ucos a) (usina)
u sin 2 a 2
u c o s
a
[Figure 1]
>x
(e)' Rm if a = 45° Note that for a given velocity ofprojection & a given horizontal range there are in general two directions of proj ection which are complement ofeach other and are equally inclined to the direction ofthe maximum range. v
^Bansal Classes
Kinematics
[2]
(F) VELOCITY & DIRECTION O F MOTION A T A GIVEN TIME :
VcosB =ucosa Squaring & adding these 2 equations we will get the velocity of the VsinB =usina-gt projectile. Dividing the velocities in y and x directions gives the direction of motion.
( g ) VELOCITY & DIRECTION O F MOTION A T A GIVEN HEIGHT H :
V cos 0 =u cos a on adding V = u - 2 gh V sin 0 =u sin a-2gh_ 2
2
2
2
2
2
2
2
2
2
( h ) EQUATIONS O F MOTION IN VECTOR NOTATION :
(i) V=u+ gt (ii) S=ut+—gt (iii) V = -=u+-gt (V = average velocity vector) 2
2
(i)
av
t
av
2.
EQUATION O F TRAJECTORY :
gx - x tan a 2u cos a v Ry dy Note that — dx represent the direction of motion 7. PROJECTILE UP AN INCLINED PLANE : (a) Total time of flight onthe inclined plane —2/ (a-P) T _ 2ug sincosp // \ s Oblique Proj ection (refer fig-1) y = x tan a -
2
2
/ —
(b)
kf
Range PQ on the inclined plane 2u cosa . sin(a-P) g cos p
PQ
2
gcos (3
2
[sin (2 a - P) - sinP]
N
(d)
W
71 u p ForMaxmimumrange 2 a - P = — =>a= —+— ^ T" Z* Hence the direction for maximum range bisects the angle between the vertical and the inclined plane. R = u
(e)
Greatest distance ofthe projectile from the inclined plane;
(c)
2
g(l+sinP)
max
u sin (a-p)
S = 2g cosp when the projectile is at H, its velocity perpendicular to the plane is zero. 8. PROJECTILE DOWN AN INCLINED PLANE: (a) Time offlight= ' ( P) 2
2
2 u s
(b) (c) (d)
faBansal Classes
n
a +
gcosp Range OP 2u sin(a + p). cosa g cos p u Maximum range= g(l-sinp) 2
2
7C _ p Angle ofproj ection a for maximum range= 4 2
Kinematics
[3]
Q.l
EXERCISE - /
A butterfly is flying with velocity 10 i +12 j m/s and wind is blowing along x axis with velocity u. If butterfly starts motionfromA and after some time reaches point B,findthe value of u.
y
B
37°
Q. 2
Find the change in velocity of the tip of the minute hand (radius =10 cm) of a clock in 45 minutes.
Q.3
A,B&Care threeobjects each movingwith constant velocity. A's speed is lOm/sec in a direction pQ. The velocity of B relative to A is 6 m/sec at an angle of, cos (15/24) to PQ. The velocity of C relative to B is 12 m/sec in a direction Qp, thenfindthe magnitude of the velocity of C. Rain is falling vertically with a speed of 20 ms" relative to air. A person is running in the rain with a velocity of 5 ms and a wind is also blowing with a speed of 15 ms (both towards east). Find the angle with the vertical at which the person should hold his umbrella so that he may not get drenched. -1
Q.4 Q.5
1
-1
-1
The velocity-time graph ofthe particle moving along a straight line is shown. The rate of acceleration and deceleration is constant and it is equal to 5 ms"" . If the s average velocity during the motion is 20 ms , thenfindthe value of t. 2
-1
25 sec
Q.6
The fig. shows the v-t graph of a particle moving in straight line. Find the time when particle returns to the starting point.
Q.7
A particle is proj ected in the X-Y plane. 2 sec after proj ection the velocity of the particle makes an angle 45° with the X - axis. 4 sec after projection, it moves horizontally. Find the velocity of projection (use g = 10 ms ).
v
-2
Q.8
A small ball rolls off the top landing of a staircase. It strikes the mid point of the first step and then mid point of the second step. The steps are smooth & identical in height & width. Find the coefficient of restitution between the ball & the first step.
Q.9
A stone is dropped from a height h. Simultaneously another stone is thrown up from the ground with such a velocity that it can reach a height of 4h. Find the time when two stones cross each other.
Q.10 A particle is proj ected upwards with a velocity of 100 m/sec at an angle of 60° with the vertical. Find the time when the particle will move perpendicular to its initial direction, taking g=10 m/sec . 2
Q.ll A particle is moving on a straight line. Its displacementfromthe initial position |s„j is plotted against time in the graph shown. What will be the velocity of the particle at 2/3 sec? Assume the graph to be a sine curve. - /
faBansal Classes
Kinematics
\time
T = 2s~
[4]
Q.12 A large number of bullets are fired in all direction with the same speed v. What is the maximum area on ground on which these bullets can spread? Q.13 A boat starts from rest from one end of a bank of a river of width d flowing with velocity u. The boat is steered with constant acceleration a in a direction perpendicular to the bank. Ifpoint of start is origin, direction ofbank is x axis and perpendicular to bank is y axis. Find the equation oftrajectory ofthe boat. Q.14 A ball is thrown horizontallyfroma cliff such that it strikes ground after 5 sec. The line of sightfromthe point of projection to the point ofhitting makes an angle of 37° with the horizontal. What is the initial velocity ofprojection. Q.15 A ball is proj ected on smooth inclined plane in direction perpendicular to line of greatest slope with velocity of 8m/s. Find it's speed after 1 sec.
8 m/s
Q.16 A glass wind screen whose inclination with the vertical can be changed, is mounted on a cart as shown infigure.The cart moves uniformly along the horizontal path with a speed of 6 m/s. At what maximum angle a to the vertical can the wind screen be placed so that the rain drops falling vertically downwards with velocity 2 m/s, do not enter the cart?
o
o
mmn777777777777777777/7777777777
Q.17 A particle is proj ectedfrompoint P with velocity 5 A/2 m/s perpendicular to the surface of a hollowrightangle cone whose axis is vertical. It collides at Q normally. Find the time ofthe flight ofthe particle.
y
t--
Q.18 Find range ofproj ectile on the inclined plane which is proj ected perpendicular to the incline plane with velocity 20m/s as shown in figure.
u = 20ms-' 37°X C- P«—X- -D A; 1.5m -B
Q.19 AB and CD are two smooth parallel walls. A child rolls a ball along ground from A towards point P find PD so that ball reaches point B after striking the wall CD. Given coefficient of restitution e = 0.5
Q.20 Initial acceleration of a particle moving in a straight line is a and initial velocity is zero. The acceleration reduces continuously to half in every t seconds as a =a . Find the terminal velocity of the particle. 2— ta0 mvuuuuummuwmv Q.21 Find the acceleration of movable pulley P and block B if rH rK acceleration of block A = 1 m/s 4-. 0
Q
2
El
)£
m
^777777777777777777777777
Q.22 The velocities of Aand B are marked inthefigure.Find the velocity of block C (assume that the pulleys are ideal and string inextensible).
3m/s lm/s
J3
B
777777777777777777777777
faBansal Classes
Kinematics
[5]
Q.23 A particle is moving in x-y plane such that x = t + sin(t) meter, y = cos (t) meter, t is the time in sec. Find the length of the path taken by the particle from t = 0 to t = 2n sec. Q.24 The speed of a particle when it is at its greatest height ^2/5 is of its speed when it is at its half the maximum height. The angle ofproj ection is and the velocity vector angle at half the maximum height is . Q.25 A weightless inextensible rope on a stationary wedge forming angle a with the horizontal. One end of the rope is fixed to the wall at point A. A small load is attached to the rope at point B. The wedge starts moving to therightwith a constant acceleration. Determine the acceleration a, ofthe load when it is still on the wedge.
777777777777/
Q.26 The horizontal range of a projectiles is R and the maximum height attained by it is H. A strong wind now begins to blow in the direction of motion of the projectile, giving it a constant horizontal acceleration = g/2. Under the same conditions ofproj ection, find the horizontal range of the proj ectile. Q .27 Consider the acceleration of a particle for a given time't' at 'a' m/s followed immediately by retardation at the same rate of'a' m/s for time 't/2', as one cycle. If the particle startedfromrest,findthe distance travelled by it after 'n' such cycles in succession. 2
2
Q. 2 8 A particle is thrown horizontally with relative velocity 10 m/sfroman inclined plane, which is also moving with acceleration 10 m/s vertically upward. Find the time after which it lands on the plane (g = 10 m/s ) ^
10m/s
2
2
faBansal Classes
Kinematics
2
3 0
[6]
EXERCISE # III
Q. 1 A steel ball bearing is releasedfromthe roof of a building. An observer standing infrontof a window 120 cm high observes that the ball takes 0.125 sec to fall from top to the bottom of the window. The ball continutes to fall & makes a completely elastic collision with side walk & reappears at the bottom of the window 2 s after passing it on the way down. How tall is the building ? Q. 2 A train takes 2 minutes to acquire its full speed 60kmphfromrest and 1 minute to come to restfromthe full speed. If somewhere in between two stations 1 km ofthe track be under repair and the limited speed on this part be fixed to 20kmph, find the late running ofthe train on account of this repair work, assuming otherwise normal at running of the train between the stations. Q. 3 A speeder in an automobile passes a stationary policeman who is hiding behind a bill board with a motorcycle. After a 2.0 sec delay (reaction time) the policeman accelerates to his maximum speed of 150 km/hr in 12 sec and catches the speeder 1.5 km beyond the billboard. Find the speed of speeder in km/hr. Q. 4
Aballoon is ascending vertically with an acceleration of 0.2m/s , Two stones are droppedfromit at an interval of 2 sec. Find the distance between them 1.5 sec after the second stone is released.(use g=9.8m/s )
Q.5
A ship steaming north at the rate of 12 km/h observes a ship due east to itself and distant 10 km, which steaming due west at the rate of 16 km/h. After what time they are at least distancefromone another and what is this least distance. An aeroplane is observed by two persons travelling at 60 km/hr in two vehicles moving in opposite directions on a straight road. To an observer in one vehicle the plane appears to cross the road track at right angles while to the observer in the other vehicle the angle appears to be 45°. At what angle does the plane actually cross the road track and what is its speed relative to the ground. A girl can paddle her canoe at 5m/sec. in still water. She wishes to cross a straight river which is flowing at 3m/sec. At what angle to the river bank should she steer to cross, (a) as quickly as possible, (b) by the shortest route. How long will aplane take to fly around a square with side a with the wind blowing at a velocity u, in the two cases the direction ofthe wind coincides with one ofthe sides the direction ofthe wind coincides with one diagonal ofthe square. The velocity ofthe plane in still air is v > u. Two ships A and B originally at a distance d from each other depart at the same time from a straight coastline. Ship A moves along a straight line perpendicular to the shore while ship B constantly heads for ship A, having at each moment the same speed as the latter. After a sufficiently great interval oftime the second ship will obviously follow thefirstone at a certain distance. Find the distance. The slopes of the wind-screen of two motorcars are p = 3 0° and p = 15° respectively. The first car is travelling with a velocity of v horizontally. The second car is travelling with a velocity v in the same direction. The hail stones are falling vertically. Both the drivers observe that the hail stones rebound vertically after elastic collision with the wind-screen. Find the ratio of v,/v A rocket is launched at an angle 53° to the horizontal with an initial speed of 100 ms . It moves along its initial line of motion with an acceleration of 30 ms~ for 3 seconds. At this time its engine falls & the rocket proceeds like afreebody. Find : the maximum altitude reached by the rocket total time of flight. the horizontal range . [ sin 53° = 4/5 ]
Q. 6 Q.7 Q. 8 (a) (b) Q. 9 Q. 10
2
2
2
t
2
r
Q. 11 (i) (ii) (iii)
^Bansal Classes
_1
2
Kinematics
[7]
Q.12 A small ball is thrown between two vertical walls such that in the absence of the wall its range would have been 5d. The angle of projection is a. Given that all the collisions are perfectly elastic, find (a) Maximum height attained by the ball. \u\uu\uuvwu\ (b) Total number of collisions before the ball comes back to the ground, and d/2 (c) Point at which the ball fallsfinally.The walls are supposed to be very tall. Q.13 A hunter is riding an elephant ofheight 4m moving in straight line with uniform speed of 2m/sec. A deer running with a speed V infrontat a distance of 4V5m moving perpendicular to the direction of motion of the elephant. If hunter can throw his spear with a speed of 1 Om/sec. relative to the elephant, then at what angle 0 to it's direction of motion must he throw his spear horizontally for a successful hit. Find also the speed 'V' ofthe deer. Q.14 A perfectly elastic ball is thrownfromthe foot of a smooth plane inclined at an angle a to the horizontal. If after striking the plane at a distance Ifromthe point of projection, it rebounds and retraces its former gl (1 + 3 sin a) path, show that the velocity of projection is 2 sin a Q.15 A particle is proj ectedfromthe foot of an inclined plane at an angle a in the vertical plane through the line of greatest slope & hits the plane at right angles. If p be the angle the direction of projection makes with the plane & if the particle returns to the point of proj ection in two jumps,findthe value ofthe coefficient ofrestitution. Q.16 A projectile is to be thrown horizontallyfromthe top of a wall of height 1.7 m. Calculate the initial velocity ofprojection if it hits perpendicularly an incline of angle 37° which startsfromthe ground at the bottom of the wall. The line of greatest slope of incline lies in the plane ofmotion of projectile. Q.17 Two inclined planes OA and OB having inclination (with horizontal) 30° and 60° respectively, intersect each other at O as shown infig.Aparticle is projected from point P with velocity u = \ 0^3 m s along a direction perpendicular to plane OA. Ifthe particle strikes plane OB perpendicularly at Q, calculate velocity with which particle strikes the plane OB, (a) (b) time offlight, (c) vertical height h of PfromO, (d) maximum heightfromO attained by the particle and (e) distance PQ Q.18 A particle is projected with a velocity 2 ^/ag so that it just clears two walls of equal height 'a' which are at a distance '2a' apart. Show that the time of passing between the walls is 2-JaJg • Q.19 A stone is projected from the point of a ground in such a direction so as to hit a bird on the top of a telegraph post of height h and then attain the maximum height 2h above the ground. If at the instant of projection, the bird were to fly away horizontally with a uniform speed, find the ratio between the horizontal velocities ofthe bird and the stone, if the stone still hits the bird while descending. Q.20 Two persons Ram and Shyam are throwing ball at each other as shown in thefigure.The maximum horizontal distancefromthe building where Ram can stand and still throw a ball at Shyam is dj. The maximum ^ horizontal distance of Ramfromthe building where Shyam can throw a ball is d . If both of them can throw ball with a velocity of ^2gk, find mm' m u u u m m fc-nn ufl m the ratio of dj/d . Neglect the height of each person. 2
_1
Shyam
2
2
faBansal Classes
Kinematics
[8]
EXERCISE # III Q. 1
The motion of a body is given by the equation = 6 . 0 - 3 v(t) ; where v (t) is the speed in m/s & t in sec., if the body has v = 0 at t = 0 then (A) the terminal speed is 2.0 m/s (B) the magnitude of the initial acceleration is 6.0 m/s (C) the speed varies with time as v(t) = 2(l -e~ )m/s (D) the speed is 1.0 m/s when the acceleration is halfthe initial value. [JEE' 1995] 2
3t
Q.2
Two guns, situated at the top of a hill of height 10 m, fire one shot each with the same speed 5 yfs m/s at; some interval oftime. One gun fires horizontally and other fires upwards at an angle of 60° with the horizontal. The shots collide in air at a point P. Find (a) the time interval between thefirings,and (b) the coordinates ofthe point P. Take origin of the coordinates system at the foot ofthe hill right below the muzzle and traj ectories in X-Y plane. [JEE' 1996]
Q. 3
The traj ectory ofa proj ectile in a vertical plane is y = ax - bx , where a, b are constants & x and y are respectively the horizontal & vertical distances ofthe projectilefromthe point ofprojection. The maximum height attained is & the angle of projectionfromthe horizontal is . [JEE' 1997]
Q.4
A large heavy box is sliding without friction down a smooth plane of inclination 9. From a point P on the bottom ofa box, a particle is proj ected inside the box. The'initial speed ofthe particle with respect to box is u and the direction of projection makes an angle a with the bottom as shown in figure. i-
(a) (b) Q.5
2
the particle lands. (Assume that the particle does not litany other surface of the box. Neglect air resistance). , ' Ifthe horizontal displacement ofthe particle as seen by an observer on the ground is zero,findthe speed of the box with respect to the ground at the instant when the particle was projected. [JEE' 1998] A particle of mass 10~ kg is moving slong the positive x-axis under the influence of a force —K F(x)= whereK= 10 Nm .Attimet = 0itisatx-1.0m&itsvelocityisv = 0. Find: 2x its velocity when itit reaches the time at which reaches xx == 0.5 0.250 mm. [JEE' 1998] In 1.0 sec. a particle goesfrompoint Ato point B moving in a semicircle ofradius 1.0 m. The magnitude of average velocity is: [JEE '99] (A) 3.14 m/sec (B) 2.0 m/sec im (C) 1.0 m/sec (D) zero BThe co-ordinates of a particle moving in a plane are given by x (t) = a cos (7it) and y (t) = b sin (rat) where a, b (
_2
(i) (ii) Q.6 Q.7
2
2
^Bansal Classes
Kinematics
[9]
Q. 8
A ball is dropped verticallyfroma height d above the ground it hits the ground and bounces up vertically to a height dl2. Neglecting subsequent motion and air resistances, its velocity v varies with the height h above the ground as [JEE'2000 (Scr)] (A)
(C)
(B)
(D)
Q.9
An object A is kept fixed at the point x = 3 m and y = 1.25 m on a plank P raised above the ground. At time t = 0 the plank starts moving along the+x direction with an acceleration 1.5 m/s . At the A same instant a stone is projectedfromthe origin with a velocity u as 1.25m shown. A stationary person on the ground observes the stone hitting the object during its downward motion at an angle of 45° to the horizontal. All the motions are in x-y plane. Find u and the time after 3.0 m oZ i which the stone hits the object. Take g = 10 m/s . [JEE 2000] Q. 10 On africtionlesshorizontal surface, assumed to be the x-y plane, a small trolley A is moving along a straight line parallel to the y-axis (seefigure)with a constant velocity of (V3 -1) m/s. At a particular instant, when the line OA makes an angle of 45° with the x-axis, a ball is thrown along the surfacefromthe origin 0. Its velocity makes an angle = — . 2
2
5
Q. 11 A particle startsfromrest. Its acceleration (a) versus time (t) is as shown a* in the figure. The maximum speed ofthe particle will be 10m/s [JEE 2004 (Scr)] (A) 110 m/s (B) 55 m/s (C) 550 m/s (D) 660 m/s 2
11
•t(s)
Q. 12 A small block slides withoutfrictiondown an inclined plane startingfromrest. Let Sn be the distance n
travelledfromtime t = n -1 to t=n. Then 7^n-l-l is S
[JEE' 2004 (Scr)]
2n 2n-l 2n - 1 2n + 1 (C) 2n + l (D) 2n + l (A) 2n (B) 2 n - l Q. 13 The velocity displacement graph of a particle moving along a straight line is shown. The most suitable acceleration-displacement graph will be v
(A)
(B)
(C)
7
TfT-X
(D) [JEE 2005 (Scr)]
faBansal Classes
Kinematics
[10]
ANSWER KEY EXERCISE # I Q.l
6m/s
Q.2
Q.4
tan (1/2)
Q.5
Q.8
3/4
Q.9
Q.12
7IV
Q.13
-1
W2I
Q.6
5s v8gy ax
r
Q.16 2tan- (l/3) ptp Q.20 /n(2) Q.23 8m
Q.17 1 sec
Q.26 R + 2H
Q.27
1
a
axi/min 36.2 sec.
Q.3
5 m/sec
Q-7
20V5 S7T
Q.10 20 sec
Q.ll
Q.14 100/3 m/s
Q.15 10 m/s
Q.18 75m
Q.19 lm
0
Q.21 a = l m / s H , a = 2 m / s t
Q.22 5 m/s
Q.24 60°, tan" ( f i f i )
Q.25 2asin(a/2)
p
2
B
1
n(3n + 4) at , Q.28 ^ sec 1
8
EXERCISE # 77 Q.l Q.4 Q.7 Q.8 Q.10 Q.12 Q.13 Q.16 Q.19
Q.2 160 sec 20.5 m Q.5 24 min, 6 km 50m (a) 90°, (b) 127° to the river flow
Q.3 Q.6
122.7 km/hr e = tan- 2,v-134.16km/h 1
2afv + V v - u l 2j2i ly2- u2 (a)' v 2 2 , ( b ) \ . Q.9 2 v -u v -u Q.ll (i) 1503.2m (ii) 35.54sec (iii) 3970.56 m 3 (a) 5d/4 tana, (b) 9, (c) point 0 V5-1 Q.15 e = — 0 = 37°, v = 6m/s 2 Q.17 (a) 10 ms , (b) 2 sec, (c) 5 m, (d) 16.25 m, (e) 20 m u=3m/s 2 lk-h V2+1 i 2
2
y
v
y
-1
Q
Q.l
A, B, C, D u sin2a Q.4 (a) gcosQ ,(b)v = Q.7 Q.6 Q.9 Q.8 A Q.12 Q.ll B 2
^Bansal Classes
2 0
+
h
EXERCISE # III
Q.3 — , tan-'a Q.2 (a) 1 sec, (b) (5 V3 m, 5 m) ucos(a + Q) Q.5 (i) V = - 1 1 m/s ( i i ) t = | + ^ cosO A, B Q.10 (a) 45°, (b) 2 m/sec u = 7.29 m/s, t = 1 sec C Q.13 B
Kinematics
[11]
BANSAL CLASSES TARGET IIT JEE 2007 XI (P,Q,R,S)
IIT-JEE SCREENING 2007 QUESTION BA NK ON
KINEMATICS Time Limit: 2 Sitting Each of 60 minutes, duration approx.
QUESTION ON There are 54 questions in this question bank.
KINEMATICS
Q. 1
A particle is moving along a curve. Then (A) if its speed is constant it has no acceleration (B) if its speed is increasing the acceleration of the particle is along its direction of motion (C) if its speed is constant the magnitude of its acceleration is proportional to its curvature. (D) the direction of its acceleration cannot be along the tangent.
Q.2
A boat having a speed of 5 km/hr. in still water, crosses a river of width 1 km along the shortest possible path in 15 minutes. The speed of the river in Km/hr. (A) 1 (B) 3 '(C) 4 (D) V41
Q.3
A block is thrown with a velocity of 2 ms~' (relative to ground) on a belt, which is moving with velocity 4 ms in opposite direction of the initial velocity of block. If the block stops slipping on the belt after 4 sec of the throwing then choose the correct statements (s) (A) Displacement with respect to ground is zero after 2.66 and displacement with respect to ground is 12 m after 4 sec. (B) Displacement with respect to ground in 4 sec is 4 m. (C) Displacement with respect to belt in 4 sec is - 12 m. (D) Displacement with respect to ground is zero in 8/3 sec.
Q.4
A particle has initial velocity 10 m/s . It moves due to constant retarding force along the line of velocity which produces a retardation of 5 m/s . Then (A) the maximum displacement in the direction of initial velocity is 10 m (B) the distance travelled in first 3 seconds is 7.5 m (C) the distance travelled in first 3 seconds is 12.5 m (D) the distance travelled in first 3 seconds is 17.5 m.
Q.5
The displacement x of a particle depend on time t as x = at - pt a (A) particle will return to its starting point after time P" 2a (B) the particle will come to rest after time ~ (C) the initial velocity of the particle was zero but its initial acceleration was not zero. a (D) no net force act on the particle at time 3P A ball is thrown from a point on ground at some angle of projection. At the same time a bird starts from a point directly above this point of projection at a height h horizontally with speed u. Given that in its flight ball just touches the bird at one point. Find the distance on ground where ball strikes
Q.6
_1
2
2
(A) 2u Q.7
1
(B)u
3
(C) 2u
(D)u
If position time graph of a particle is sine curve as shown, what will be its velocity-time graph. (B)
<6BansalClasses
(C)
Question Bank on Kinematics
m
Q.8
A truck starting from rest moves with an acceleration of 5 m/s for 1 sec and then moves with constant velocity. The velocity w.r.t ground v/s time graph for block in truck is (Assume that block does not fall off the truck) 2
(A) Q.9
5 m/s
(B)
(C)
3ms
H L d i = 0.2 TST i® Psewtio (D)None of these
5 m/s
If angular velocity of a disc depends an angle rotated 0 as co = 0 + 20, then its angular acceleration a at 0 = 1 rad is : (A) 8 rad/sec (B) 10 rad/sec (C) 12 rad/sec '' (D) None 2
2
2
2
Q.10 Two particles start simultaneously from the same point and move along two straight lines, one with uniform velocity v and other with a uniform acceleration a. If a is the angle between the lines of motion of two particles then the least value of relative velocity will be at time given by (A) (v/a) sin a (B)(v/a)cosa (C)(v/a)tana (D)(v/a)cota Q.ll If a particle takes t second less and acquires a velocity of v ms"" more in falling through the same distance (starting from rest) on two planets where the accelerations due to gravity are 2 g and 8 g respectively then: (A) v = 2gt (B) v = 4gt (C) v = 5 gt (D) v = 16 gt 1
Q.12 At a given instant, A is moving with velocity of 5m/s upwards. What is velocity of B at that time : (A) 15 m/s ^ (B) 15 m/s t (C) 5 m/s I (D) 5 m/s t Q.13 It takes one minute for a passenger standing on an escalator to reach .ac top. If the escalator does not move it takes him 3 minute to walk up . How long will it take fo. uie passenger to arrive at the top if he walks up the moving escalator ? (A) 30 sec (B) 45 sec (C) 40 sec t D) 35 sec Q.14 The co-ordinates of a moving particle at a time t, are give by, x = 5 sin 101, y = 5 cos 1 Ot. The speed of the particle is : (A) 25 " (B) 50 (G) 10
(D) None
Q. 15 Tangential acceleration of a particle moving in a circle of radius 1 m varies with time t as (initial velocity of particle is zero). Time after which total acceleration oi particle makes and urgl of 30° with radial acceleration is (A) 4 sec (B) 4/3 sec (C) 2 sec (D) ^2 m
s e c
time (sec)
Q.16 A particle is proj ected from a horizontal plane (x-z plane) such that its velocity vector at time t is given by V = ai + (b - ct) j • Its range on the horizontal plane is given by 3ba 2ba ba (D) None (C) (B) (A)
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Question Bank on Kinematics
[3]
Q.17 v-t graph of an obj ect of mass 1 kg is shown (A) net work done on the object in 30 sec is zero. (B) the average acceleration of the object is zero. (C) the average velocity of the object is zero. (D) the average force on the object is zero.
v (m/s)
20-10--
10
20
30 t(sec)
Q. 18 A projectile of mass 1 kg is projected with a velocity of V20 m/s such that it strikes on the same level as the point of projection at a distance of V3 m. Which of the following options are incorrect: (A) the maximum height reached by the projectile can be 0.25 m. (B) the minimum velocity during its motion can be Vl5 m/s (C) the minimum time taken for the flight can be sec. (D) maximum potential energy during its motion can be 6J. Q. 19 Velocity-time graph for a car is semicircle as shown here. Which of the following is correct: (A) Car must move in circular path. (B) Acceleration of car is never zero, (C) Mean speed ofthe particle is n/2 m/s. (D) The car makes a turn once during its motion.
V1
lm/s 2 sec
Q.20 A ball is projected from top of a tower with a velocity of 5 m/s at an angle of 53° to horizontal. Its speed when it is at a height of 0.45 m from the point of projection is : (A) 2 m/s (B) 3 m/s (C)4m/s (D) data insufficient. Q.21 A particle moves along a straight line in such a way that it's acceleration is increasing at the rate of 2 m/s . It's initial acceleration and velocity were 0, the distance,covered by it in t = 3 second is. (A) 27 m (B) 9 m (C) 3 m (D) 1 m 3
Q.22 A flag is mounted on a car moving due North with velocity of 20 km/hr. Strong winds are blowing due East with velocity of 20 km/hr. The flag will point in direction (A) East (B) North - East (C) South - East (D) South - West Q.23 A ball is thrown vertically down with velocity of 5m/s. With what velocity should another ball be thrown down after 2 seconds so that it can hit the 1 ball in 2 seconds (A) 40 m/s (B) 55 m/s (C) 15 m/s (D) 25 m/s st
B Q.24 A man is crossing a river flowing with velocity of 5 m/s. He reaches a point' directly across at a distance of 60 m in 5 sec. His velocity in still water should be \T=5 / 60 m (A) 12 m/s (B) 13 m/s — (C) 5 m/s (D) 10 m/s m s
Q. 2 5 Average velocity of a particle is proj ectile motion between its starting point and the highest point of its trajectory is: (projection speed = u, angle of projection from horizontal 0) (A) u cosG
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(B) ^Vl + 3cos 9 2
(C) ^•V'2 + COS 0 2
Question Bank on Kinematics
(D) U
+ COS
m
Q.26 Find time of flight of projectile thrown horizontally with speed 50 ms from a long inclined plane which makes an angle of 6 = 45° from horizontal. (A) 10V2 sec (B) 20V2 sec (C) 10 sec (D) 5-Jl sec -1
Q.27 Particle is dropped from the height of 20m from horizontal ground. There is wind blowing due to which horizontal acceleration of the particle becomes 6 ms . Find the horizontal displacement of the particle till it reaches ground. (A) 6 m (B)10m (C) 12 m (D) 24 m -2
Q.28 A bail is dropped from height 5m. The time after which ball stops rebounding if coefficient of restitution between ball and ground e = 1/2, is (A) 1 sec (B) 2 sec (C) 3 sec (D) infinite Q.29 A ball is hit by a batsman at an angle of 37° as shown in figure. The man standing at P should run at what minimum velocity so that he catches the ball before it strikes the ground. Assume that height of man is negligible in comparison to maximum height of projectile. (A) 3 ms" (B) 5 ms" (C) 9 ms(D) 12 ms" 1
1
Q.30 Find the velocity of the hanging block if the velocities of the free ends of the rope are as indicated in the figure. (A) 3/2 m/s t (B) 3/2 m/s I (C) 1/2 m/s T (D) 1/2 m/s 4
2m/s
IU.LJJ1I
mi.""
lm/s •
Q.31 A man swimming down stream overcome a float at a point M. After travelling distance D he turned back and passed the float at-a distance of D/2 from the point M, then the ratio of speed of swimmer with respect to still water to the speed of the river will be (A) 2 (B) 3 (C) 4 (D) 2.5 Q.32 Choose the correct alternative (s) (A) If the greatest height to which a man can throw a stone is h, then the greatest horizontal distance upto which he can throw the stone is 2h-. (B) The angle of projection for a projectile motion whose range R is n times the maximum height is tan (4/n) (C) The time of flight T and the horizontal range R of a projectile are connected by the equation gT = 2Rtan9 v. here 0 is the angle of projection. (D) A ball is thrown vertically up. Another ball is thrown at an angle 0 with the vertical. Both of them remain in air for the same period of time. Then the ratio of heights attained by the two balls 1:1. -1
2
Q.33 Acceleration versus velocity graph ofa particle moving in a straight line starting from rest is as shown in figure. The corresponding velocity-time graph would be (A)
1*1
(B)
(D)
Question Bank on G r a v i t a t i o n
[5]
Q.34 Aparticle is projected vertically upwards from a point Aon the ground. It takes t time to reach a point B but it still continues to move up. If it takes further tj time to reach the ground from point B then height of point Bfromthe ground is 1
(A) | g ( t ! + t ) (C)|g(t,+t y (B) g t, t (D) ™ g t , t . Q.35 Mark the correct statements for a particle going on a straight line (A) if the velocity is zero at any instant, the acceleration should also be zero at that instant (B) if the velocity is zero for a time interval, the acceleration is zero at any instant within the time interval (C) if the velocity and acceleration have opposite sign, the object is slowing down (D) if the position and velocity have opposite sign, the particle is moving towards the origin 2
2
2
2
Q.36 A projectile is fired with a speed u at an angle 0 with the horizontal. Its speed when its direction of motion makes an angle 'a' with the horizontal is (A) u sec0 cosa (B) u sec0 sina (C) u cos0 seca (D) u sin 0 seca Q.37 Balls are thrown vertically upward in such a way that the next ball is thrown when the previous one is at the maximum height. If the maximum height is 5m, the number of balls thrown per minute will be (A) 40 (B) 50 (C) 60 (D) 120 Q.38 A projectile is fired with a velocity at right angle to the slope which is inclined at an angle 0 with the horizontal. The expression for the range R along the incline is 2v 2v 2v sec© (B) - t a n 0 (C) tan0 sec 0 (D) -—tan 0 (A) 2
: i :
2
Q.39 A bead is free to slide down a smooth wire tightly stretched between points A and B on a vertical circle. If the bead starts from rest at A, the highest point on the Gircle (A) its velocity v on arriving at B is proportional to cos0 (B) its velocity v on arriving at B is proportional to tan0 (C) time to arrive at B is proportional to cos0 (D) time to arrive at B is independent of 0 Q.40 The velocity- time graph of a body falling from rest under gravity and rebounding from a solid surface is represented by which ofthe following graphs? v v (D) (C) (B). (A) -»t -> t Q.41 A disc arranged in a vertical plane has two groves of same length directed along the vertical chord AB and CD as shown inthefig.The same particles slide down along AB and CD. The ratio of the time t /t is (A) 1 : 2 (B) 1 : V2 (C) 2 : 1 (D) 4 l • 1 AB
CD
Q.42 The magnitude of displacement of a particle moving in a circle of radius a with constant angular speed co varies with time t as cot (D) 2a cos cot (C) 2a cos cot (B) 2a sin(A) 2 a sincot
1*1
Question Bank on G r a v i t a t i o n
[6]
Q.43 A glass wind screen whose inclination with the vertical can be changed is mounted on a car. The car moves horizontally with a speed of 2m/s. At what angle a with the vertical should the wind screen be placed so that the rain drops falling vertically downwards with velocity 6 m/s strike the wind screen perpendicularly. (A) tan-'(3) (B) tan- (l/3) (C) cos-'P) (D) s u r ^ l ^ ) Q.44 A particle is projected vertically upwards from O with velocity v and a second particle is projected at the same instant from P (at a height h above O) with velocity v at an angle of projection 0. The time when the distance between them is minimum is h (C) h/v (D) h/2v (A) 2vsin0 (B) 2vcos0 Q.45 A body moves with velocity v = / n x m/s where x is its position. The net force acting on body is zero at: (A) 0 m (B) x = e m (C) x = e m (D) x = 1 m Q.46 Wind is blowing in the north direction at speed of 2 m/s which causes the rain to fall at some angle with the vertical. With what velocity should a cyclist drive so that the rain appears vertical to him : (A) 2 m/s south (B) 2 m/s north (C) 4 m/s west (D) 4 m/s south Q.47 A body A is thrown vertically upwards with such a velocity that it reaches a maximum height of h. Simultaneously another body B is dropped from height h. It strikes the ground and does not rebound. The velocity of A relative to B v/s time graph is best represented by : (upward direction is positive) !
2
(A)
(B)
V a b
(C)
V a b
' AB
(D)
VAB
t!
Q.48 A body of mass 1 kg is acted upon by a force F = 2 sin 37rt i + 3 cos 3 ret j find its position at t = 1 sec if at t = 0 it is at rest at origin. f 3 2^ r2 2 ^ f 2 2 ) (D) none of these (A) L37t ' 9TT J (B) L 37r ' 3n ) (C) L3TT ' 3tc J 2
2
2
2
2
Q.49 A force F = Be acts on a particle whose mass is m and whose velocity is 0 at t = 0. It's terminal velocity is: C. B BC B (A) mB (B) mC ( D ) - mC ( Q m— y Q.50 A man moves in x-y plane along the path shown. At what point is c his average velocity vector in the same direction as his instantaneous velocity vector. The man starts from point P. A (A) A (B)B (C)C (D) D Ct
Q.51 From the velocity time garph of a particle moving in straight line decide which of the following is incorrect statement. (A) the particle crosses its initial position (B) the speed ofthe particle increases continuously (C) the force on the particle is constant (D) the acceleration of the particle is constant.
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Question Bank on Kinematics
t v
m
Q. 5 2 If T is the total time of flight, h is the maximum height & R is the range for horizontal motion, the x & y co-ordinates of projectile motion and time t are related as: (A) y - 4 h ( i ) ( . - i )
(B)y = 4 h ( ! )
( O y = 4h ( ! ) ( , - ! )
-4h(|)(.-| y
Q.53 A particle initially at rest is subjected to two forces . One is constant, the other is a retarding force proportional to the particle velocity . In the subsequent motion of the particle : (A) the acceleration will increase from zero to a constant value (B) the acceleration will decrease from its initial value to zero (C) the velocity will increase from zero to maximum & then decrease (D) the velocity will increase from zero to a constant value. Q.54 A ball is projected from ground with a velocity V at an angle 9 to the vertical. On its path it makes an elastic collison with a vertical wall and returns to ground. The total time of flight ofthe ball is 2vsin9 2vcos9 vsin29 vcos9 (A) - y (B) - 7 (C) — ( ° )
ANSWERKEY Q.3
B, C, D
Q.4
A, C
Q-7
C
Q.8
C
Q.l
C, D
Q.2
B
Q.5
A, B, C, D
Q.6
C
Q.9
C
Q.10 B
Q.ll B
Q.12 A
Q.13 B
Q.14 B
Q.15 C
Q.16 B
Q.17 A, B, D
Q.l 8 D
Q.19 C
Q.20 C
Q.21 B
Q.22 C
Q.23 A
Q.24 B
Q.25 B
Q.26 C
Q.27 C
Q.28 C
Q.29 B
Q.30 A
Q.31 B
Q.32 A, B, C, D
Q.33 D
Q.34 D
Q.35 B,C,D
Q.36 C
Q.37 C
Q.38 C
Q.39 A, D
Q.40 A
Q.41 B
Q.42 B
Q.43 A
Q.44 D
Q.45 D
Q.46 B
Q.47 C
Q.48 C
Q.49 B
Q.50 C
Q.51 B
Q.52 A,B
Q.53 B,D
Q.54 B
1*1
Question Bank on G r a v i t a t i o n
[8]
