Question

A body is rotating about its own axis. Its rotational kinetic energy is ' x ' and its angular momentum is ' \(y\) '. Hence its moment of inertia about its own axis is

• A. \(\frac{x^{2}}{2y}\)
• B. \(\frac{y^{2}}{2x}\)
• C. \(\frac{x}{2y}\)
• D. \(\frac{y}{2x}\)

Hint:

Express both kinetic energy and angular momentum in terms of I and omega, then eliminate omega.

Answer 1

The Correct Option is B

Step 1: Understanding the Concept
Rotational kinetic energy \(x=\frac{1}{2}I\omega^2\) and angular momentum \(y=I\omega\).

Step 2: Eliminate omega
From \(y=I\omega\), \(\omega=\frac{y}{I}\).

Step 3: Substitute
\(x=\frac{1}{2}I\frac{y^2}{I^2}=\frac{y^2}{2I}\), so \(I=\frac{y^2}{2x}\).

Step 4: Compare the options
This is option (B).

Final Answer:
The moment of inertia is \(\frac{y^2}{2x}\). \[ \boxed{\text{(B) }\dfrac{y^{2}}{2x}} \]