First slide

Dynamics of rotational motion about fixed axis

Question

A solid sphere of mass m and radius R is rotating about its diameter. A solid cylinder of the same mass and same radius is also rotating about its geometrical axis with an angular speed twice that of the sphere. The ratio of their kinetic energies of rotation $(E_{sphere} / E_{cylinder})$ will be

Moderate

A

2:3
B

1:5
C

1:4
D

3:1

Solution

$\frac{E_{Sphere}}{E_{Cylinder}} = \frac{\frac{1}{2} I_{s} ω_{s}^{2}}{\frac{1}{2} I_{c} ω_{c}^{2}} = \frac{I_{s} ω_{s}^{2}}{I_{c} ω_{c}^{2}}$
$Here, I_{s} = \frac{2}{5} m R^{2}, I_{c} = \frac{1}{2} m R^{2}$
$\begin{array}{l} ω_{c} = 2 ω_{s} \\ \frac{E_{Sphere}}{E_{Cylinder}} = \frac{\frac{2}{5} m R^{2} \times ω_{s}^{2}}{\frac{1}{2} m R^{2} \times {(2 ω_{s})}^{2}} = \frac{4}{5} \times \frac{1}{4} = \frac{1}{5} \end{array}$

Get Instant Solutions

When in doubt download our app. Now available Google Play Store- Doubts App

Recieve an sms with download link

Doubts App

OR

SCAN ME

Doubts App

Doubts App