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Chapter 7 System of particles and Rotational Motion Solutions

Question - 31 : - A solid disc and a ring, both of radius 10 cm areplaced on horizontal table simultaneously, with initial angular speed equal to10 π rad s-2. Which of the two willstart to roll earlier ? The co-efficient of kinetic friction is μk = 0.2.

Answer - 31 : - Force of friction (μk  mg) produces an acceleration a in the center ofmass (moving with υ = R ω)

Question - 32 : - A cylinder of mass 10 kg and radius 15 cm is rollingperfectly on a plane of inclination 30°. The co-efllcient of the staticfriction μs = 0.25.
(a) How much is the force of friction acting on the cylinder ?
(b) What is the work done against friction during rolling ?
(c) If the inclination 6 of the plane is increased, at what value of 6 does thecylinder begin to skid, and not roll perfectly ?

Answer - 32 : - Here M = 10 kg ; R = 15 cm = 0.15 m ; μs= 0.25 ; 9 = 30°

Question - 33 : - Read each statement belowcarefully, and state, with reason, if is true or false :
(a)During rolling, the force of friction acts in the same’direction as thedirection of motion of the CM of th body.
(b) The instantaneous speed of the point of contact during rolling is zero.
(c) The instantaneous acceleration of the point of contact during rolling iszero.
(d) For prefect rolling motion, work done against friction is zero.
(e) A wheel moving down a perfectly frictionless inclined plane will undergoslipping (not rolling) motion.

Answer - 33 : -

(a) True (The forceof friction helps in rolling a body).
(b) True (Arolling body is considered as a rotating body about an axis passing through thepoint of cotact).
(c) False (Sincethe body is rotating, so its instantaneous acceleration cannot be zero).
(d) True (Sincepoint of contact is at rest, so work done is zero).
(e)True (In case of frictionless inclined plane, there is notangential force of friction (or torque) and hence wheel cannot roll).

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