### NEET Solved Paper 2018 Question 31

##### 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 [NEET - 2018]

#### 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:

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} $