JEE Main 2022 · Physics · Rotational Motion · easy

A uniform disc of mass 6 kg and radius 1 m rotates freely about its central axis at 10 rad s^-1. A lump of clay of mass 2 kg is dropped gently onto…

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A uniform disc of mass

6\ \mathrm{kg}

and radius

1\ \mathrm{m}

rotates freely about its central axis at

10\ \mathrm{rad\,s^{-1}}

. A lump of clay of mass

2\ \mathrm{kg}

is dropped gently onto its rim and sticks there. The loss of kinetic energy in the process is

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Answer: (B) $60\ \mathrm{J}$

No external torque acts about the axis, so angular momentum is conserved:

I_1\omega_1=(I_1+mR^{2})\omega_2

with

I_1=\frac12(6)(1)^2=3\ \mathrm{kg\,m^2}

. Hence

3(10)=(3+2)\omega_2

and

\omega_2=6\ \mathrm{rad\,s^{-1}}

. Initial KE

=\frac12(3)(100)=150\ \mathrm{J}

; final KE

=\frac12(5)(36)=90\ \mathrm{J}

. Loss

=60\ \mathrm{J}

(dissipated in the sticking). Angular momentum is conserved but kinetic energy is not in such an inelastic process.

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