Rotational Motion Question 90
Question: 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
Options:
A) $ {W_B}\text{}{W_A}\text{}{W_C} $
B) $ {W_A}\text{}{W_B}\text{}{W_C} $
C) $ {W_C}\text{}{W_B}\text{}{W_A} $
D) $ {W_A}\text{}{W_C}\text{}{W_B} $
Show Answer
Answer:
Correct Answer: C
Solution:
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[c] Work done required to bring them rest
$ \Delta \text{W=}\Delta KE $
$ \Delta W=\frac{1}{2}|{{\omega }^{2}} $
$ \Delta W\propto l $ for same $ \omega $
$ {W_A}\text{:}{W_B}\text{:}{W_C}\text{=}\frac{2}{5}M{R^{2}}\text{:}\frac{1}{2}M{R^{2}}\text{:M}{R^{2}} $
$ \text{=}\frac{2}{5}:\frac{1}{2}:1 $
$ =4:5:10 $
$ \Rightarrow {W_C}\text{}{W_B}\text{}{W_A} $
