#### Nature of Physical World and Measurement-1 marks, 2 marks, 3 marks, 5 marks.

11th Standard

Reg.No. :
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Physics

Time : 02:00:00 Hrs
Total Marks : 100
Part-A
15 x 1 = 15
1. A uniform force of (2$\hat { i }$+$\hat { j }$) N acts on a particle of mass 1 kg. The particle displaces from position (3$\hat { j }$+$\hat { k }$) m to (5$\hat { i }$+3$\hat { j }$) m. The work done by the force on the particle is

(a)

9 J

(b)

6 J

(c)

10 J

(d)

12 J

2. A ball of mass 1 kg and another of mass 2kg are dropped from a tall building whose height is 80 m. After, a fall of 40 m each towards Earth, their respective kinetic energies will be in the ratio of

(a)

$\sqrt2:1$

(b)

$1:\sqrt2$

(c)

2:1

(d)

1:2

3. A body of mass 1 kg is thrown upwards with a velocity 20 ms-1 It momentarily comes to rest after attaining a height of 18 m. How much energy is lost due to air friction?(Take g = 10 ms-2)

(a)

20 J

(b)

30 J

(c)

40 J

(d)

10 J

4. A body of mass 4 m is lying in xy-plane at rest. It suddenly explodes into three pieces. Two pieces each of mass m move perpendicular to each other with equal speed v. The total kinetic energy generated due to explosion is

(a)

mv2

(b)

$\frac{3}{2}$mv2

(c)

2mv2

(d)

4mv2

5. The potential energy of a system increases, if work is done

(a)

by the system against a conservative force

(b)

by the system against a non-conservative force

(c)

upon the system by a conservative force

(d)

upon the system by a non- conservative force

6. What is the minimum velocity with which a body of mass m must enter a vertical loop of radius R so that it can complete the loop?

(a)

$\sqrt{2gR}$

(b)

$\sqrt{3gR}$

(c)

$\sqrt{5gR}$

(d)

$\sqrt{gR}$

7. The work done by the conservative force for a closed path is

(a)

always negative

(b)

zero

(c)

always positive

(d)

not defined

8. If the linear momentum of the object is increased by 0.1% then the kinetic energy is Increased by

(a)

0.1 %

(b)

0.2 %

(c)

0.4 %

(d)

0.01 %

9. If the potential energy of the particle is $\alpha -\frac { \beta }{ 2 } { x }^{ 2 }$ then force experienced by the particle is

(a)

F=$\frac { \beta }{ 2 } { x }^{ 2 }$

(b)

F=βx

(c)

F=-βx

(d)

F=-$\frac { \beta }{ 2 } { x }^{ 2 }$

10. A wind-powered generator converts wind U(x) energy into electric energy. Assume that the generator converts a fixed fraction of the wind energy intercepted by its blades into electrical energy. For wind speed v, the electrical power output will be proportional to,

(a)

v

(b)

v2

(c)

v3

(d)

v4

11. A particle is placed at the origin and a force F = kx is acting on it (where k is a positive constant). If U (0) = 0, the graph of U(x) versus x will be (where U, is the potential , energy function)

(a)

(b)

(c)

(d)

12. A particle which is constrained to move along x-axis, is subjected to a force in the same direction which varies with the distance x of the particle from the origin as F(x) =kx + ax3. Here, k and a are positive constants. For x≥0, the functional form of the potential, energy U(x) of the particles

(a)

(b)

(c)

(d)

13. A spring of force constant k is cut into two pieces such that one piece is double the length of the other. Then, the long piece will have a force constant of

(a)

$\frac{2}{3}$k

(b)

$\frac{3}{2}$k

(c)

3k

(d)

6k

14. An engine pumps water continuously through a hose. Water leaves the hose with a velocity v and m is the mass per unit length of the water of the jet. What is the rate at which kinetic energy is imparted to water?

(a)

${{1}\over{2}}{m}{v}^{2}$

(b)

mv3

(c)

${{1}\over{2}}{m}{v}^{3}$

(d)

${{1}\over{2}}{m}{v}^{2}$

15. Two equal masses m1 and m2 moving along the same straight line with velocities + 3 m/s and -5 m/s respectively collide elastically. Their velocities after the collision will be respectively

(a)

- 4 m/s and +4 m/s

(b)

+4 m/s for both

(c)

- 3 m/s and +5 m/s

(d)

- 5 m/s and + 3 m/s

16. 12 x 2 = 24
17. Explain how the definition of work in physics is different from general perception

18. Write the various types of potential energy. Explain the formulae.

19. Write the differences between conservative and Non-conservative forces. Give two examples each.

20. Explain the characteristics of elastic and inelastic collision.

21. Define the following
a) Coefficient of restitution
b) Power
c) Law of conservation of energy
d) loss of kinetic energy in inelastic collision

22. Show that the ratio of velocities of equal masses in an inelastic collision when one of the masses is stationary is $\frac { { v }_{ 1 } }{ { v }_{ 2 } } =\frac { 1-e }{ 1+e }$

23. A body of mass 5 kg is thrown up vertically with a kinetic energy of 1000 J. If acceleration due to gravity is 10 ms-1, find the height at which the kinetic energy becomes half of the original value.

24. Two bodies of mass 60 kg and 30 kg move in the same direction along straight line with velocity 40 cms-1 and 30 cms-1 respectively suffer one dimensional elastic collision. Find their velocities after collision.

25. A particle of mass 70 g moving at 50 cms-1 is acted upon by a variable force as shown in the figure. What will be its speed once the force stops?

26. A particle strikes a horizontal frictionless floor with a speed u at an angle $\theta$  with the vertical and rebounds with the speed v at an angle $\phi$ with an vertical. The coefficient of restitution between the particle and floor is e. What is the magnitude of v?

27. A particle of mass m is fixed to one end of a light spring of force constant k and unstretched length I. It is rotated with an angular velocity w in horizontal circle. What will be the length increase in the spring?

28. A gun fires 8 bullets per second into a target X. If the mass of each bullet is 3 g and its speed 600 s-1. Then, calculate the power delivered by the bullets.

29. 12 x 3 = 36
30. How will you measure the work done? When
(i) the force acts along the direction of motion of the body and,
(ii) the force is inclined to the direction of motion of the body?

31. A weight lifter lifts a mass of 250 kg with a force 5000 N to the height of 5m
(a) What is the work done by the weight lifter?
(b) What is the work done by the gravity?
(c) What is the net work done on the object?

32. Two objects of masses 2 kg and 4 kg are moving with the same momentum of 20 kg m s-1
(a) Will they have same kinetic energy?
(b) Will they have same speed?

33. An object of mass 2 kg is taken to a height 5 m from the ground (g = 10 ms-2 ).
(a) Calculate the potential energy stored in the object.
(b) Where does this potential energy come from?
(c) What external force must act to bring the mass to that height?
(d) What is the net force that acts on the object while the object is taken to the height 'h'?

34. Let the two springs A and B be such that kA > kB, On which spring will more work has to be done if they are stretched by the same force?

35. 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).

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

37. Consider an object of mass 2 kg moved by an external force 20 N in a surface having coefficient of kinetic friction 0.9 to a distance 10 m. What is the work done by the external force and kinetic friction? Comment on the result. (Assume g = 10 ms-2)

38. A body of mass 100 kg is lifted to a height 10 m from the ground in two different ways as shown in the figure. What is the work done by the gravity in both the cases? Why is it easier to take the object through a ramp?

39. An object of mass 2 kg attached to a spring is moved to a distance x = 10 m from its equilibrium position. The spring constant k = 1N m-1 and assume that the surface is frictionless.
(a) When the mass crosses the equilibrium position, what is the speed of the mass?
(b) What is the force that acts on the object when the mass crosses the equilibrium position and extreme position x = ± 10m?

40. A vehicle of mass 1250 kg is driven with an acceleration 0.2 along a straight level road against an external resistive force 500 N. Calculate the power delivered by the vehicle's engine if the velocity of the vehicle is 30 ms-1.

41. A lighter particle moving with a speed of 10 ms-1 collides with an object of double its mass moving in the same direction with half its speed. Assume that the collision is a one dimensional elastic collision. What will be the speed of both particles after the collision?

42. 5 x 5 = 25
43. Explain with graphs the difference between work done by a constant force and by a variable force

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

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

46. Arrive at an expression for elastic collision in one Dimension and discuss various cases.

47. What is inelastic collision? In which way it is different from elastic collision. Mention few examples in day to day life for inelastic collision.