Q.1. Should the centre of mass of a body necessarily lie inside the body? Explain.
AnswerAnswer: No, it may lie outside the body. In case of semicircular ring, it is at the centre which is outside the ring.
Q.2. What physical quantities do the following represent?
(a) Moment of linear momentum
(b) Rate of change of angular momentum
(c) The product of moment of inertia and angular acceleration?
AnswerAnswer: (a) Angular momentum (b)Torque (c) Torque (τ = Iα)
Q.3. Which component of linear momentum does not contribute to angular momentum?
AnswerAnswer: Radial component as it is perpendicular to angular momentum.
Q.4. With reference to figure of a cube of edge a and mass m, state whether the following are true or false. (O is the centre of the cube.)
Q.5. Why the moment of inertia of a solid disc is smaller than that of a ring of same size and mass?
AnswerAnswer: Since the entire mass of the ring is concentrated at its circumference, so, it is at maximum distance from the centre but for the disc it is uniformly distributed over its area.
Q.6. With reference to figure of a cube of edge a and mass m, state whether the following are true or false. (O is the centre of the cube.)
AnswerAnswer: (a) False, perpendicular axis theorem is applicable only to a lamina. (b) True (c) False, z and z” are not parallel axes. (d) True.
Q.7. Two solid spheres of same mass are made up of different metals (ρ1 > ρ2). Which of them has a larger M.I. about its diameter?
AnswerAnswer: The 2nd sphere is made up of a metal of lower density so its size will be bigger than the first. So the 2nd sphere will have large M.I.
Q.8. Which one has a larger M.I. and why?
(a) a hollow sphere
(b) a solid sphere of same mass and radius and why?
AnswerAnswer: The hollow sphere has a large M.I. as its mass is distributed on its surface and away from the axis of rotation.
Q.9. A big and a small sphere roll down from rest through an inclined plane. Which one goes to the bottom first?
AnswerAnswer: Since the acceleration due to gravity is independent of mass so both of them will reach the bottom simultaneously.
Q.10. Why the spin angular velocity of a neutron star increases tremendously as it is formed from a star collapsing under its own gravitational pull?
AnswerAnswer: As the star collapses under its own gravitational pull, size of the star decreases. So its M.I. decreases. As its angular momentum remains constant (L = Iω) , so, its angular velocity increases.
Q.11. State the condition for translational equilibrium of a body.
AnswerAnswer: For translational equilibrium of a body net force acting on it i.e., the vector sum of all the forces acting on the body must be zero.
Q.12. State the condition for rotational equilibrium of a body.
AnswerAnswer: For rotational equilibrium of a body the vector sum of torques of all the forces acting on the body about the reference point must be zero.
Q.13. When the earth shrinks, without reducing its mass, what change will be there in the duration of a day?
AnswerAnswer: L is conserved. If the earth shrinks, duration of the day decreases.
Q.14. Why are the spokes fitted in a cycle wheel?
AnswerAnswer: To increase moment of inertia with less mass.
Q.15. Why ships which have been emptied of cargo are filled with ballast (sand/water)?
AnswerAnswer: Centre of mass is lowered to have more stability by loading ballast.
Q.16. Explain how a cat is able to land on its feet after a fall taking advantage of the principle of conservation of angular momentum?
AnswerAnswer: While falling a cat stretches its body along with the tail so that its moment of inertia (I) increases. As no external torque acts, L = Iω = constant. As I increase w decreases and it lands gently on its feet.
Q.17. A rifle barrel has a spiral groove which imparts spin to the bullet. Why?
AnswerAnswer: Angular momentum gained by the bullet provides better accuracy.
Q.18. Why are we not able to rotate a wheel by pulling or pushing along its radius?