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NEET generalGeneralMedium

Question

A solid sphere is in rolling motion. In rolling motion a body possesses translational kinetic energy (KtK_t) as well as rotational kinetic energy (KrK_r) simultaneously. The ratio Kt:(Kt+Kr)K_t : (K_t + K_r) for the sphere is

1

10:710 : 7

2

5:75 : 7

3

7:107 : 10

4

2:52 : 5

Step-by-Step Solution

Kt=12mv2K_t = \frac{1}{2}mv^2. Kt+Kr=12mv2+12Iω2=12mv2+12(25mr2)(vr)2=710mv2K_t + K_r = \frac{1}{2}mv^2 + \frac{1}{2}I\omega^2 = \frac{1}{2}mv^2 + \frac{1}{2}(\frac{2}{5}mr^2)(\frac{v}{r})^2 = \frac{7}{10}mv^2. Therefore, KtKt+Kr=1/27/10=57\frac{K_t}{K_t + K_r} = \frac{1/2}{7/10} = \frac{5}{7}.

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.

generalsphererollingmotionrollingmotion

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