Question

A solid sphere of mass 2 kg and radius 50 cm is rotating about its diameter with an angular speed of $50 rad s^{-1}$. The angular momentum of the sphere is

• A. 50 Js
• B. 10 Js
• C. 25 Js
• D. 20 Js

Hint:

Always convert units to SI (meters for radius) before calculation. $50 \text{ cm} \rightarrow 0.5 \text{ m}$.

Answer 1

The Correct Option is B

Step 1: Formula for Angular Momentum:
Angular Momentum ($L$) is the product of the Moment of Inertia ($I$) and Angular Velocity ($\omega$). \[ L = I\omega \] For a solid sphere rotating about its diameter, the Moment of Inertia is: \[ I = \frac{2}{5} MR^2 \]
Step 2: Calculate Moment of Inertia ($I$):
Given: Mass $M = 2$ kg, Radius $R = 50$ cm $= 0.5$ m. \[ I = \frac{2}{5} \times 2 \times (0.5)^2 \] \[ I = 0.8 \times 0.25 \] \[ I = 0.2 \, kg m^2 \]
Step 3: Calculate Angular Momentum ($L$):
Given: Angular speed $\omega = 50 \, rad s^{-1}$. \[ L = I \times \omega \] \[ L = 0.2 \times 50 \] \[ L = 10 \, kg m^2 s^{-1} \text{ (or Js)} \]
Step 4: Final Answer:
The angular momentum is 10 Js.