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NEET generalGeneralMedium

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 ω\omega about their own symmetry axes. The amounts of work (W) required to bring them to rest, would satisfy the relation

1

WB>WA>WCW_B > W_A > W_C

2

WA>WB>WCW_A > W_B > W_C

3

WC>WB>WAW_C > W_B > W_A

4

WA>WC>WBW_A > W_C > W_B

Step-by-Step Solution

Work done required to bring them to rest is ΔW=ΔKE=12Iω2\Delta W = \Delta KE = \frac{1}{2} I \omega^2. Since ω\omega is same, ΔWI\Delta W \propto I. The moments of inertia are IA=25MR2I_A = \frac{2}{5}MR^2, IB=12MR2I_B = \frac{1}{2}MR^2, IC=MR2I_C = MR^2. Thus, WA:WB:WC=25:12:1=4:5:10W_A : W_B : W_C = \frac{2}{5} : \frac{1}{2} : 1 = 4 : 5 : 10. Therefore, WC>WB>WAW_C > W_B > W_A.

Exam Context & Concepts Covered

This question aligns with the NEET general syllabus, specifically targeting concepts from General. Mastering this topic is crucial for scoring well in the upcoming medical entrance examinations. Solving conceptually related problems will help you understand the nuances of these concepts and improve your problem-solving speed.

generalobjectsspherecircularcircularradius

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