JEE Main 2025 — Rotational Motion Question with Solution

Step 1: Use the Torque Formula

The force pulls the rim and creates a turning effect called torque. The formula for torque is: torque = force × radius (F × R).

Step 2: Relate Torque to Angular Acceleration

Torque is also described as: torque = moment of inertia × angular acceleration (I × α).

Step 3: Set Up the Equation

Set the two expressions for torque equal. So, $F\times R=I\times \alpha$.

Step 4: Solve for Moment of Inertia $I$

$I=\frac{F\times R}{\alpha }$

Step 5: Substitute the Values

Here, the force $F=10\mathrm{N}$, the radius $R=0.2\mathrm{m}$, and the angular acceleration $\alpha =2{rad/s}^2$.

Step 6: Calculate

$I=\frac{10\times 0.2}{2}=\frac{2}{2}=1{\mathrm{kg}\mathrm{m}}^2$

So, the moment of inertia of the wheel is $1{\mathrm{kg}\mathrm{m}}^2$.