JEE Main 2021 · Physics · Rotational Motion · medium

A horizontal uniform disc of mass 8 kg and radius 1 m rotates freely about its vertical axis at 10 rad s^-1. A 1 kg lump of putty is gently dropped…

Numerical answer

A horizontal uniform disc of mass

8\ \mathrm{kg}

and radius

1\ \mathrm{m}

rotates freely about its vertical axis at

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

. A

1\ \mathrm{kg}

lump of putty is gently dropped on the disc at its rim and sticks there. The loss of kinetic energy, in joules, is

Show answer and solution

Answer: 40

I_{disc}=\tfrac12MR^2=4\ \mathrm{kg\,m^2}

. Angular momentum is conserved:

4(10)=(4+1)\omega'\Rightarrow\omega'=8\ \mathrm{rad\,s^{-1}}

. Initial KE

=\tfrac12(4)(100)=200\ \mathrm{J}

; final KE

=\tfrac12(5)(64)=160\ \mathrm{J}

. Loss

=40\ \mathrm{J}

(the energy goes into the inelastic sticking).

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