A4 Laws of Motion DCP

1. The diagram shows a rough plank resting on a c ylinder with one end of the plank on rough ground. Neglect friction between plank and cylinder. Draw diagram to show: (a) The forces acting in the plank, (b) The forces acting in the cylinder.

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2. Two spheres A and B are placed between two vertical walls as shown in fig. F riction is absent everywhere. Draw the free body diagrams of both the spheres. Key: Sol:

2. Two spheres A and B are placed between two vertical walls as shown in fig. F riction is absent everywhere. Draw the free body diagrams of both the spheres. Key: Sol:

3. A point A on a sphere of weight W rests in contact with w ith a smooth vertical wall and is supported by a string joining a point B on the sphere to a point C on the wall. Draw free body diagram of the sphere.

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4. Write down the components of four forces  F1 , F2 , F 3  and  F 4  along ox and oy directions as shown fig. 5.33.

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5. A uniform rod AB of weight W is hinged to a fixed point at A. It is held in the horizontal position by a string, one end of which is attached to B as shown fig. find in te rms of W, the tension in the string. Key: Sol:

6. In question 3 of the same exercise the radius of the sphere is a. The length of the string is also a. Find tension in the string. Key: Sol:

7. Find the values of the unknown forces if the given set of forces shown in fig. are in equilibrium.

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8. Two beads of equal masses m are attached by a string of length

2a  and free to move in a

smooth circular ring lying in a vertical plane as shown fig. Here, a is the radius of the ring. Find the tension and acceleration of B just after the beads are released to move.

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1. Three blocks of mass 1 kg, 4 kg and 2 kg are placed on a smooth horizontal plane as shown fig. Find: (a) The acceleration of the system (b) The normal force between 1 kg block and 4 kg block, (c) The net force on 2 kg block.

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2. Two blocks of mass 2 kg and 4 kg are released from rest over a smooth inclined plane of 0

inclination 30  as shown fig. what is the normal force between the two blocks?

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3. What should be the acceleration ‘a’ of the box shown in fig so that the block of mass m exerts a force

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mg  4

 on the floor of the box?

4. A plumb bob of mass 1 kg is hung from the ceiling of a train compartment. The t rain moves on 0

an inclined plane with constant velocity. If the angle of incline is 30 . Find the angle made by the 2

string with the normal to the ceiling. Also, the tension in the string. ( g=10m/s  ) Key: Sol:

5. Repeat both parts of the above question, if t he train moves with an acceleration a= plane. Key: Sol:

 g  2

 up the

6. Two blocks of mass 1kg and 2 kg are connected by a string AB of mass 1 kg. The blocks ar e placed on a smooth horizontal surface. Block of mass 1 kg is pulled by a horizontal force F o f magnitude 8 N. Find the tension in the str ing at points A and B.

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1. In figure m1 = 1kg and m 2 = 4kg . Find the mass M of the hanging block which will prevent the smaller block from slipping over the triangular block. All the surfaces are frictionless and the strings and the pulleysare light.

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2. A 2 kg object is slide along the frictionless floor with initial velocity (10 m/ s) i  (a) Describe the motion of the object relative to car (b) when does the object reach its original position relative to the box car.

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3. A 2 kg object is slide along the frictionless floor with initial velocity (10 m/ s) k  . Describe the motion (a) in car’s frame (b) in ground frame.

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4. A 2 k object is slid along a rough floor (cefficient of sliding friction = 0.3) with initial velocity (10 m/s ) i . Describe the motion of the object relative to car assuming that the coefficient of static friction is greater than 0.5.

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