Essential University Physics: Volume 1 (4th Edition)

Published by Pearson
ISBN 10: 0-134-98855-8
ISBN 13: 978-0-13498-855-9

Chapter 10 - Exercises and Problems - Page 192: 36

Answer

This ball is a hollow sphere.

Work Step by Step

Let's assume, mass of the ball = M Radius of the ball = R Speed of the ball = V = $r\omega$ We can write, Translational kinetic energy $(K_{1})= \frac{1}{2}MV^{2}$ Rotational kinetic energy $(K_{2})= \frac{1}{2}I\omega^{2}$ $K_{2}=\frac{1}{2}I\frac{V^{2}}{R^{2}}-(1)$ Given that, Total kinetic energy $(K)=K_{1}+K_{2}=100\space J-(2)$ $K_{2}=40\space J-(3)$ $(2)=\gt (1)$ $K_{1}=100\space J-40\space J=60\space J$ $ \frac{1}{2}MV^{2}=60=\gt V^{2}=\frac{120}{M}$ $(3)=\gt (1)$ $40=\frac{1}{2R^{2}}I\times\frac{120}{M}$ $I=\frac{2}{3}MR^{2}$ This equation is equal to the rotational inertia of a hollow sphere. So this ball is a hollow sphere
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