JEE Main 2024 · Physics · Rotational Motion · medium

A circular platform of mass 80 kg and radius 2 m rotates freely about its vertical axis at 2 rad s^-1. A boy of mass 40 kg standing at its rim walks…

Numerical answer

A circular platform of mass

80\ \mathrm{kg}

and radius

2\ \mathrm{m}

rotates freely about its vertical axis at

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

. A boy of mass

40\ \mathrm{kg}

standing at its rim walks slowly to the centre. The work done by the boy (in J) is

Show answer and solution

Answer: 640

Initially

I_1=\tfrac12(80)(2)^2+40(2)^2=160+160=320\ \mathrm{kg\,m^2}

. At the centre the boy contributes nothing:

I_2=160\ \mathrm{kg\,m^2}

. Angular momentum is conserved, so

\omega_2=\dfrac{320\times2}{160}=4\ \mathrm{rad\,s^{-1}}

. The boy's work equals the increase in kinetic energy:

\tfrac12(160)(4)^2-\tfrac12(320)(2)^2=1280-640=640\ \mathrm{J}

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