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

Hint:

Combine K = (1/2) I w^2 and L = I w to eliminate w.

Answer 1

The Correct Option is D

Step 1: Dimension check:
Energy has units kg m$^2$ s$^{-2}$ and angular momentum kg m$^2$ s$^{-1}$. We want kg m$^2$.

Step 2: Test $y^2/x$:
$\frac{(\text{kg m}^2\text{s}^{-1})^2}{\text{kg m}^2\text{s}^{-2}} = \text{kg m}^2$. The units work.

Step 3: Fix the constant:
Using $x = \frac{y^2}{2I}$ gives the factor of 2: $I = \frac{y^2}{2x}$.

Final Answer:
Option (D) is correct. \[ \boxed{\frac{y^2}{2x}} \]