Physics Q28 – JEE-MAIN 2025

Home Physics Rotational MotionQuestion #445

A cord of negligible mass is wound around the rim of a wheel supported by spokes with negligible mass. The mass of wheel is

10 kg

and radius is

10 cm

and it can freely rotate without any friction. Initially the wheel is at rest. If a steady pull of

20 N

is applied on the cord, the angular velocity of the wheel, after the cord is unwound by

1 m

, would be :

Clue 1 of 3: Rotational Dynamics

This problem involves the application of a constant force causing rotational motion, so consider the relationship between torque, moment of inertia, and angular acceleration.

🥷

Ninja Strategy•Eliminate Obvious Impossibilities

Quickly rule out options that are physically impossible given the problem description, such as zero velocity when motion is clearly occurring.

🧠 Full Solution Path

● Video Walkthrough

Step 1: Calculate Moment of Inertia and Torque✦ Active

Given mass $M = 10 kg$ and radius $R = 10 cm = 0.1 m$ . Since the cord is wound around the rim of a wheel supported by spokes, we assume the moment of inertia is that of a ring:

I = M R^{2} = (10 kg) (0.1 m)^{2} = 0.1 {kg m}^{2}

The applied force is $F = 20 N$ . The torque produced by this force is:

τ = F \times R = (20 N) (0.1 m) = 2 N m

Step 2: Determine Angular Acceleration and Displacement○ Expand

Using Newton's second law for rotation, $τ = I α$ , we find the angular acceleration:

α = \frac{τ}{I} = \frac{2 N m}{0.1 {kg m}^{2}} = 20 {rad/s}^{2}

The cord unwinds by $s = 1 m$ . The corresponding angular displacement is:

θ = \frac{s}{R} = \frac{1 m}{0.1 m} = 10 rad

💡 Teacher's Secret Hint

Ensure you use the correct moment of inertia based on the description of the wheel.

Step 3: Calculate Final Angular Velocity○ Expand

Since the wheel starts from rest, its initial angular velocity is $ω_{0} = 0$ . Using the rotational kinematic equation:

ω^{2} = ω_{0}^{2} + 2 α θ

Substitute the values:

ω^{2} = 0^{2} + 2 (20 {rad/s}^{2}) (10 rad) = 400 {rad}^{2} / s^{2}

Therefore, the final angular velocity is:

ω = \sqrt{400} = 20 rad/s

💡 Teacher's Secret Hint

Double-check your calculations for angular acceleration and displacement before the final kinematic step.

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Physics Question 28 – JEE-MAIN 2025

Clue 1 of 3: Rotational Dynamics

🧠 Full Solution Path