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

Hint:

The moment of inertia can be determined by rearranging the formula for rotational kinetic energy and using the relationship between kinetic energy and angular momentum.

Answer 1

The Correct Option is B

Step 1: Understanding the Question:
We are given rotational kinetic energy \( K \) and angular momentum \( L \) and need to find the moment of inertia \( I \) in terms of these variables.
Step 2: Key Formula or Approach:
The relationship between \( K \), \( L \), and \( I \) is:
\[ K = \frac{L^2}{2I} \]
Step 3: Detailed Explanation:
Given \( K = x \) and \( L = y \).
Substitute into the formula:
\[ x = \frac{y^2}{2I} \]
Rearranging for \( I \):
\[ I = \frac{y^2}{2x} \]
Step 4: Final Answer:
The moment of inertia is \( \frac{y^2}{2x} \).