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NEET · Physics · STD 11 - 6. system of particles and rotational motion

Three objects, \(A :\) (a solid sphere), \(B :\) (a thin circular disk) and \(C :\) (a circular ring), each have the same mass \(M\) and radius \(R.\) They all spin with the same angular speed \(\omega\) about their own symmetry axes. The amounts of work \((W)\) required to bring them to rest, would satisfy the relation

  1. A \(W_C>W_B>W_A\)
  2. B \(W_A>W_B>W_C\)
  3. C \(W_A>W_C>W_B\)
  4. D \(W_B>W_A>W_C\)
Verified Solution

Answer & Solution

Correct Answer

(A) \(W_C>W_B>W_A\)

Step-by-step Solution

Detailed explanation

       Work done required to bring a object to rest \(\Delta W = \Delta KE\) \(\begin{array}{l}
\Delta W = \frac{1}{2}I{\omega ^2}\,;\,where\,I\, = moment\,of\,inertia\\
For\,same\,\omega ,\,\Delta W \propto I\\
For\,a\,solid\,sphere,\,{I_A} = \frac{2}{5}M{R^2}\\
For\,a\,thin\,cicular\,disk,\,{I_B} = \frac{1}{2}M{R^2}\\
For\,a\,circular\,ring,\,{I_c} = M{R^2}\\
\therefore \,\,{I_c} > {I_B} > {I_A}\,\,\therefore \,\,{W_c} > {W_B} > {W_A}
\end{array}\)