#### Important 5mark -chapter 3,4

11th Standard

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Physics

Use blue pen Only

Time : 01:00:00 Hrs
Total Marks : 200

Part A

40 x 5 = 200
1. Briefly explain the origin of friction. Show that in an inclined plane, angle of friction is equal to angle of repose

2. Briefly explain 'centrifugal force' with suitable examples.

3. A force of 50N act on the object of mass 20 kg. shown in the figure. Calculate the acceleration of the object in x and y directions.

4. A bob attached to the string oscillates back and forth. Resolve the forces acting on the bob into components. What is the acceleration experience by the bob at an angle ፀ

5. Two masses m1 and m2 are connected with a string passing over a frictionless pulley fixed at the corner of the table as shown in the figure. The coefficient of static friction of mass m1 with the table is μs, Calculate the minimum mass m3 that may be placed on m1 to prevent it from sliding.Check if m1=15 kg, m2=10 kg,m3= 25 and μs = 0.2

6. Apply Lami's theorem on sling shot and calculate the tension in each string?

7. Find the impulse of a constant force and variable force with diagrams.

8. Imagine that the gravitational force between Earth and Moon is provided by an invisible string that exists between the Moon and Earth. What is the tension that exists in this invisible string due to Earth's centripetal force? (Mass of the Moon = 7.34$\times$1022 kg, Distance between Moon and Earth = 3.84 $\times$ 108m)

9. Two bodies of masses 15 kg and 10 kg are connected with light string kept on a smooth surface. A horizontal force F=500 N is applied to a 15 kg as shown in the figure. Calculate the tension acting in the string

10. A car takes a turn with velocity 50 ms-1 on the circular road of radius of curvature 10m. calculate the centrifugal force experienced by a person of mass 60kg inside the car?

11. Describe Galileo's experiments concerning motion of objects on inclined planes?

12. Prove Impulse - Momentum equation.

13. Show how impulse force can be measured graphically.

14. What happens to the object at rest if (i) fs = 0 (ii) fs = Fext (iii) fs = max.

15. Using Newton's laws calculate the tension acting on the mango (mass m = 400g) hanging from a tree.

16. Briefly explain how is a horse able to pull a cart.

17. Derive an expression for the acceleration of the body sliding down a frictionless surface.

18. Two masses m1 and m2 m1 > m2 or in contact with each other on a smooth horizontal surface. Calculate the magnitude of contact force between them.

19. Briefly explain how is a vehicle able to go round a level curved track. Determine the maximum speed with which the vehicle can negotiate this curved track safely.

20. As shown In the diagram, three blocks connected together lie on a horizontal frictionless table and pulled to the right with a force F = 50N. If m1 = 5 kg, m2 = 10 kg and m3 = 15 kg. Find the tensions T1 and T2.

21. State and explain work energy principle. Mention any three examples for it.

22. Arrive at an expression for power and velocity. Give some examples for the same.

23. A bob of mass m is attached to one end of the rod of negligible mass and length r, the other end of which is pivoted freely at a fixed center O as shown in the figure. What initial speed must be given to the object to reach the top of the circle? (Hint: Use law of conservation of energy). Is this -speed less or greater than speed obtained in the section 4.2.9?

24. Two different unknown masses A and B collide. A is initially at rest when B has a speed v. After collision B has a speed v/2 and moves at right angles to its original direction of motion. Find the direction in which A moves after collision

25. A body of mass of 3 kg initially at rest makes under the action of an applied horizontally force of 10 N on a table with co-efficient of kinetic friction = 0.3, then what is the workdone by the applied force in 10s:

26. Find the workdone if a particle moves from position $\vec { { r }_{ 1 } } =(2\overset { \wedge }{ i } +\overset { \wedge }{ j } -\overset { \wedge }{ 3k } )$ to a position $\vec { { r }_{ 2 } } =(4\overset { \wedge }{ i } +6\overset { \wedge }{ j } -7\overset { \wedge }{ k } )$ under the effect of force $\vec {F } =(3\overset { \wedge }{ i } +2\overset { \wedge }{ j } -\overset { \wedge }{ 4k } )$N.

27. Calculate work done to move a boy of mass 20 kg along an inclined plane ($\theta$ = 45°) with constent velocity through a distance of 10 m.

28. A bullet of mass 25 g moving with a velocity of 400 ms-1 strikes a cardboard and goes out from the other end with a velocity of 300 ms-1, find out the work done in passing through the cardboard.

29. Find the work done in moving a particle along a vectors $\vec { s } =(\overset { \wedge }{ i } -2\overset { \wedge }{ j } +3\overset { \wedge }{ k } )$m if applied force is $\vec { F } =(2\overset { \wedge }{ i } -3\overset { \wedge }{ j } +4\overset { \wedge }{ k } )$N.

30. Find the workdone in moving a particle along a vectors $\vec { S } =(\overset { \wedge }{ i } -2\overset { \wedge }{ j } +6\overset { \wedge }{ k } )$  m if applied force is $\vec { F } =(2\overset { \wedge }{ i } +3\overset { \wedge }{ j } +\overset { \wedge }{ 5k } )$ N at an angle 60°.

31. A body of mass 600 g travels in a straight line with velocity v=a$\times \frac{3}{2}$ . a=3m-1/4s-1 What is the workdone by the net force during its displacement from x = 0 to x = 3 m?

32. A body of mass 500 g initially at rest is moved by a horizontal force of 1 N. Calculate the workdone by the force in 20s and show that is equal to the change in kinetic energy of the body.

33. Find the work done in pulling and pushing another though 200 m horizontally when a force of 1000N is acting along a chain making an angle of 60° with ground. Assume the floor to be smooth friction less surface.

34. Two springs have spring constant k1 and k2 (k1 > k2) on which spring is more work done, if
(i) They are stretched by the same force.
(ii) They are stretched by same amount.

35. Derive an expression for the gravitational potential energy of a body of mass 'm' raised to a height 'h' above the earth's surface.

36. If an object of mass 2 kg is thrown up from the ground reaches a height of 5 m and falls back to the Earth (neglect the air resistance). Calculate
(a) The work done by gravity when the object reaches 5 m height
(b) The work done by gravity when the object comes back to Earth
(c) Total work done by gravity both in upward and downward motion and mention the physical significance of the result.

37. A body of mass m is attached to the spring which is elongated to 25 cm by an applied force from its equilibrium position.
(a) Calculate the potential energy stored in the spring-mass system?
(b) What is the work done by the spring force in this elongation?
(c) Suppose the spring is compressed to the same 25 cm, calculate the potential energy stored and also the work done by the spring force during compression. (The spring constant, k= 0.1 N m-1).

38. Compute the work done by the gravitational force for the following cases

39. An object of mass 1 kg is falling from the height h = 10m. Calculate
(a) The total energy of an object at h = 10 m.
(b) Potential energy ofthe object when it is at h = 4 m.
(c) Kinetic energy of the object when it is at h = 4 m.
(d) What will be the speed of the object when it hits the ground?
(Assume g = 10 m s-2)

40. An object of mass m is projected from the ground with initial speed v0. Find the speed at height h.