#### Important 2mark -chapter 5,6

11th Standard

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Physics

Use blue pen Only

Time : 01:00:00 Hrs
Total Marks : 178

Part A

Answer all the questions

89 x 2 = 178
1. What is meant by an internal force & external force?

2. What is rigid body?

3. Define the center of mass of a body.

4. What is point mass?

5. State the rule which is used to find the direction of torque.

6. How will you find the direction of rotation using the direction of torque?

7. When does the body have precession?

8. State the torque about an axis is independent of the origin.

9. State law of Conservation of angular momentum.

10. What is the effect of Torque on Rigid Bodies.

11. Obtain an expression for the power delivered by torque.

12. What is meant by rolling friction?

13. Calculate moment of inertia with respect to rotational axis xx' in following figures (a) and (b).

14. Four bodies of masses 5 kg, 2 kg, 3 kg and 4 kg are respectively placed at position (0, 0, 0), (2, 0, 0) (0, 3, 0) and (-2, -2, 0) calculate the moment of inertia about x-axls, y-axis and z-axis.

15. Adjoining diagram has three disc, in which each has mass M and radius R. Find the moment of inertia of this system about axis xx'.

16. Two rings have their moments of inertia in the ratio of 4 :1 and their diameters are in the ratio of 4 :1. Find the ratio of their masses.

17. The power output of an automobile engine is advertised to be 200 hp at 600 rpm. What is the corresponding torque?

18. In the following figure radii r1 and r2 are 10 cm and 20 cm respectively. If the moment of inertia of the wheel is 1500 kg m2, then determine its angular acceleration

19. Find the torque of a  force $7\widehat { i } -3\widehat { j } -5\widehat { k }$ about the origin which acts on a particle  whose position vector is $\widehat { i } +\widehat { j } -\widehat { k }$

20. A wheel of mass 8 kg and radius of gyration 25cm is rotating at 300 rpm what is its moment of inertia.

21. Calculate the moment of inertia of the earth about its diameter taking It to be a sphere of 1025 kg and diameter 12800 km.

22. A body of mass 50g is revolving about an axis in a circular path. The distance of the centre of mass of the body from the axis of rotation is 50cm. Find the moment of inertia of the body.

23. A thin metal hoop of radius 0.25m and mass 2 kg starts from rest and rolls down an inclined plane. If its linear velocity on reaching the foot of the plane is 2 ms-1, what is its rotational K.E.at that instant?

24. A torque of 2.0 x 10-4 Nm is applied to produce an angular acceleration of 4 rad S-2 in a rotating body. What is the moment of inertia of the body?

25. Some heavy boxes are to be loaded along with some empty boxes on a cart. Which boxes should be put on the cart first and why?

26. About which axis, the moment of inertia of a body is minimum?

27. A cat is able to land on its feet after a fall. Why?

28. Two boys of the same weight sit at the opposite ends of a diameter of a rotating circular table. What happens to the speed of rotation if they move nearer to axis of rotation?

29. What is the power needed to maintain uniform circular motion?

30. Why centripetal force cannot do work?

31. A particle moves in a circular path with decreasing speed. What happens to its angular momentum?

32. Give examples where the centre of mass coincides with the geometrical centre of the body.

33. The distance between the centres of carbon and oxygen atoms in the carbon monoxide gas molecule is 1.13 $\mathring{A}$ . Locate the centre of mass of the gas molecule relative to the carbon atom.

34. Three blocks of uniform thickness and masses m, m and 2m are placed at three corners of a triangle having co-ordinates (2.5, 1.5) (3.5, 1.5) and (3, 3) respectively. Find the centre of mass of the system.

35. Two identical particles move towards each other with velocity 2 v and v respectively. The velocity of centre of mass?

36. Should the centre of mass of a body necessarily lie inside the body?

37. Is centre of mass a reality?

38. Why in hand driven grinding machine, handle is put near the circumference of the stone or wheel?

39. A labourer standing near the top of an old wooden step ladder feels unstable. Why?

40. If no external torque acts on a body, will its angular velocity remain conserved?

41. The bottom of a ship is made heavy. Why?

42. A ball tied to a string takes 4s to complete revolution along a horizontal circle. If by pulling the cord, the radius of the circle is reduced to half of the previous value, then how much time the ball will take in one revolution.

43. If angular momentum is conserved in a system whose moment of inertia is decreased, will its rotational kinetic energy be conserved?

44. A particle performing uniform circular motion has angular. momentum L. What will be the new angular momentum, if its angular frequency is doubled and its kinetic energy halved?

45. A solid cylinder of mass 20 kg rotates about its axis with angular speed 100 rad s-1. The radius of the cylinder is 0.25m. What is the kinetic energy associated with the rotation of the cylinder? What is the magnitude of angular momentum of the cylinder about its axis?

46. Keeping the mass of earth constant, if its radius is halved then what will be the duration of the day and night?

47. Explain with reason why if ice melts at pole then moment of inertia of earth increases, angular velocity ω decreases and day-night will be longer?

48. What is a rigid body?

49. When an object will have precession? Give one example.

50. When an angular momentum of the object will be zero?

51. When an object be in mechanical equilibrium?

52. A boy sits near the edge of revolving circular disc
(i) What will be the change in the motion of a disc?
(ii) If the boy starts moving from edge to the center of the disc, what will happen?

53. Are moment of inertia and radius of gyration of a body constant quantities?

54. A cat is able to land on its feet after a fall. Which principle of physics is being used? Explain.

55. About which axis a uniform cube will have minimum moment of inertia ?

56. State the principle of moments of rotational equilibrium.

57. Write down the moment of inertia of a disc of radius R and mass m about an axis in its plane at a distance R/2 from its centre

58. Can the couple acting on a rigid body produce translator motion?

59. Which component of linear momentum does not contribute to angular momentum?

60. A system is in stable equilibrium. What can we say about its potential energy ?

61. Is radius of gyration a constant quantity ?

62. Two solid spheres of the same mass are made of metals of different densities. Which of them has a large moment of inertia about the diameter?

63. The moment of inertia of two rotating bodies A and Bare IA and IB ( CA> IB) and their angular momenta are equal. Which one has a greater kinetic energy?

64. A particle moves on a circular path with decreasing speed. What happens to its angular momentum?

65. What is the value of instantaneous speed of the point of contact during pure rolling?

66. Which physical quantity is conserved when a planet revolves around the sun?

67. What is the value of torque on the planet due to the gravitational force of sun?

68. If no external torque acts on a body, will its angular velocity be constant?

69. Why there are two propellers in a helicopter?

70. A child sits stationary at one end of a long trolley moving uniformly with speed V on a smooth horizontal floor. If the child gets up and runs about on the trolley in any manner, then what is the effect of the speed of the centre of mass of the (trolley + child) system?

71. A solid sphere of mass 20 kg and radius 0.25 m rotates about an axis passing through the center. What is the angular momentum if the angular velocity is 5 rad s-1.

72. If a comet suddenly hits the Moon and imparts energy which is more than the total energy of the Moon, what will happen?

73. If the Earth’s pull on the Moon suddenly disappears, what will happen to the Moon?

74. If the Earth has no tilt, what happens to the seasons of the Earth?

75. An unknown planet orbits the Sun with distance twice the semi-major axis distance of the Earth’s orbit. If the Earth’s time period is T1, what is the time period of this unknown planet?

76. Assume that you are in another solar system and provided with the set of data given below consisting of the planets’ semi-major axes and time periods. Can you infer the relation connecting semi-major axis and time period?

Planet
(imaginary)
Time period(T)
(in year)
Semi major axis (a)
(in AU)
Kurinji 2 8
Mullai 3 18
Marutham 4 32
Neithal 5 50
Paalai 6 72
77. If the masses and mutual distance between the two objects are doubled, what is the change in the gravitational force between them?

78. Two bodies of masses m and 4m are placed at a distance r. Calculate the gravitational potential at a point on the line joining them where the gravitational field is zero.

79. If the ratio of the orbital distance of two planets ${d_1\over d_2}=2,$ what is the ratio of gravitational fi eld experienced by these two planets?

80. The Moon Io orbits Jupiter once in 1.769 days. The orbital radius of the Moon Io is 421700 km. Calculate the mass of Jupiter?

81. If the angular momentum of a planet is given by $\vec{L}=5t^2\hat i-6t\hat j+3\hat k$ . What is the torque experienced by the planet? Will the torque be in the same direction as that of the angular momentum?

82. Four particles, each of mass M and equidistant from each other, move along a circle of radius R under the action of their mutual gravitational attraction. Calculate the speed of each particle

83. Suppose unknowingly you wrote the universal gravitational constant value as G = 6.67 x 1011 instead of the correct value G = 6.67 x 1011, what is the acceleration due to gravity g' for this incorrect G? According to this new acceleration due to gravity, what will be your weight W'?

84. Calculate the gravitational field at point O due to three masses m1, m2 and m3 whose positions are given by the following figure. If the masses m1 and m2 are equal what is the change in gravitational field at the point O?

85. What is the gravitational potential energy of the Earth and Sun? The Earth to Sun distance is around 150 million km. The mass of the Earth is 5.9 × 1024 kg and mass of the Sun is 1.9 × 1030 kg.

86. Earth revolves around the Sun at 30 km s−1. Calculate the kinetic energy of the Earth. In the previous example you calculated the potential energy of the Earth. What is the total energy of the Earth in that case? Is the total energy positive? Give reasons.

87. An object is thrown from Earth in such a way that it reaches a point at infinity with non-zero kinetic energy [K.E(r=$\infty$)= ${1\over 2}MV_{\infty}^2$], with what velocity should the object be thrown from Earth?

88. Suppose we go 200 km above and below the surface of the Earth, what are the g values at these two points? In which case, is the value of g small?

89. Calculate the change in g value in your district of Tamilnadu. (Hint: Get the latitude of your district of Tamilnadu from the Google). What is the difference in g values at Chennai and Kanyakumari?