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Q.

A particle of mass ‘m’ is attached to the rim of a uniform disc of mass ‘m’ and radius R. The disc is rolling without slipping on a stationary horizontal surface, as shown in the figure. At a particular instant, the particle is at the top most position and centre of the disc has speed $v_{0}$ and its angular speed $ω$ . Choose the CORRECT option(s)regarding the motion of the system (disc + particle) at that instant.

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a

$|\vec{V_{C}} - \vec{V_{B}}| = |\vec{V_{B}} - \vec{V_{D}}|$

b

$v_{0} = ωR$

c

Kinetic energy of the system is $\frac{11}{4} {mv}_{0}^{2}$

d

Speed of point mass m is less than $2 v_{0}$

answer is A, B, D.

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Detailed Solution

$K = K_{D} + K_{P}$

$= \frac{1}{2} {mv}_{0}^{2} (1 + \frac{1}{2}) + \frac{1}{2} m {(2 V_{0})}^{2} = \frac{11}{4} {mV}_{0}^{2}$

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A particle of mass ‘m’ is attached to the rim of a uniform disc of mass ‘m’ and radius R. The disc is rolling without slipping on a stationary horizontal surface, as shown in the figure. At a particular instant, the particle is at the top most position and centre of the disc has speed v0 and its angular speed ω. Choose the CORRECT option(s)regarding the motion of the system (disc + particle) at that instant.