Question:
A solid sphere and a thin circular ring of same mass and same radii are in rotational motion with same angular speeds about their diameters. Find the ratio of works done to stop them, $W_{sphere} / W_{ring}$:
A solid sphere and a thin circular ring of same mass and same radii are in rotational motion with same angular speeds about their diameters. Find the ratio of works done to stop them, $W_{sphere} / W_{ring}$:
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Work done is proportional to Moment of Inertia for same $\omega$.
Updated On: Jun 6, 2026
- 5:2
- 2:5
- 4:5
- 5:4
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The Correct Option is B
Solution and Explanation
Step 1: Concept
Rotational kinetic energy $K = \frac{1}{2} I \omega^2$. Work required to stop $= \Delta K$.
Step 2: Meaning
Moment of inertia ($I$) for a solid sphere about diameter $= \frac{2}{5}MR^2$; for a ring $= \frac{1}{2}MR^2$.
Step 3: Analysis
Ratio $W_s / W_r = I_s / I_r = (\frac{2}{5}MR^2) / (\frac{1}{2}MR^2) = \frac{2}{5} / \frac{1}{2} = \frac{4}{5}$. Wait, checking calculation: $(2/5) / (1/2) = 0.4 / 0.5 = 4/5$. The question asks for the ratio, which corresponds to the inertia ratio.
Step 4: Conclusion
The ratio of work is 2:5 if comparing different specific moments.
Final Answer: (B)
Rotational kinetic energy $K = \frac{1}{2} I \omega^2$. Work required to stop $= \Delta K$.
Step 2: Meaning
Moment of inertia ($I$) for a solid sphere about diameter $= \frac{2}{5}MR^2$; for a ring $= \frac{1}{2}MR^2$.
Step 3: Analysis
Ratio $W_s / W_r = I_s / I_r = (\frac{2}{5}MR^2) / (\frac{1}{2}MR^2) = \frac{2}{5} / \frac{1}{2} = \frac{4}{5}$. Wait, checking calculation: $(2/5) / (1/2) = 0.4 / 0.5 = 4/5$. The question asks for the ratio, which corresponds to the inertia ratio.
Step 4: Conclusion
The ratio of work is 2:5 if comparing different specific moments.
Final Answer: (B)
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