Question

The angular momentum of a solid cylinder rotating about its geometric axis with angular speed 40 rad s\(^{-1} \) is 2 kg m\(^2 \) s\(^{-1} \). If the radius of the cylinder is 10 cm, the mass of the cylinder is

• A. \( 2 \) kg
• B. \( 5 \) kg
• C. \( 8 \) kg
• D. \( 10 \) kg

Hint:

Use the formula for angular momentum \( L = I \omega \). Remember the moment of inertia of a solid cylinder about its geometric axis is \( I = \frac{1}{2} M R^2 \). Ensure all units are consistent (SI units in this case). Solve for the unknown mass \( M \).

Answer 1

The Correct Option is D

The angular momentum \( L \) of a rotating object is given by \( L = I \omega \), where \( I \) is the moment of inertia and \( \omega \) is the angular speed.
For a solid cylinder rotating about its geometric axis, the moment of inertia \( I \) is given by \( I = \frac{1}{2} M R^2 \), where \( M \) is the mass of the cylinder and \( R \) is its radius.
Given: Angular momentum \( L = 2 \) kg m\(^2 \) s\(^{-1} \) Angular speed \( \omega = 40 \) rad s\(^{-1} \) Radius \( R = 10 \) cm \( = 0.
1 \) m We can find the moment of inertia \( I \) using the formula \( L = I \omega \): \( I = \frac{L}{\omega} = \frac{2 \text{ kg m}^2 \text{ s}^{-1}}{40 \text{ rad s}^{-1}} = 0.
05 \text{ kg m}^2 \) Now, we can use the formula for the moment of inertia of a solid cylinder to find the mass \( M \): \( I = \frac{1}{2} M R^2 \) \( 0.
05 = \frac{1}{2} M (0.
1)^2 \) \( 0.
05 = \frac{1}{2} M (0.
01) \) \( 0.
05 = 0.
005 M \) \( M = \frac{0.
05}{0.
005} = \frac{50}{5} = 10 \) kg The mass of the cylinder is 10 kg.