Physics Q30 – JEE-MAIN 2026

Home Physics Rotational MotionQuestion #433

A wheel initially at rest is subjected to a uniform angular acceleration about its axis. In the first 2 s it rotates through an angle

θ_{1}

and in the next 2 s it rotates through an angle

θ_{2}

. The ratio

\frac{θ_{2}}{θ_{1}}

is _______.

Clue 1 of 3: Kinematics of Rotational Motion

Recall the equations of rotational motion for constant angular acceleration.

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Step 1: Identify the Governing Kinematic Equation✦ Active

The wheel starts from rest, so its initial angular velocity is $ω_{0} = 0$ . It undergoes uniform angular acceleration $α$ . The angular displacement $θ$ is given by the kinematic equation:

θ = ω_{0} t + \frac{1}{2} α t^{2}

Since $ω_{0} = 0$ , the equation simplifies to:

θ = \frac{1}{2} α t^{2}

Step 2: Calculate Angular Displacement for the First Interval○ Expand

For the first 2 seconds ( $t = 2$ s), the angular displacement is $θ_{1}$ :

θ_{1} = \frac{1}{2} α (2 s)^{2} = \frac{1}{2} α (4) = 2 α

Step 3: Calculate Angular Displacement for the Second Interval and the Ratio○ Expand

The total time elapsed for both intervals is $2 s + 2 s = 4 s$ . The total angular displacement in 4 seconds, from rest, is:

θ_{total} = \frac{1}{2} α (4 s)^{2} = \frac{1}{2} α (16) = 8 α

The angular displacement in the *next* 2 seconds, $θ_{2}$ , is the difference between the total displacement in 4 seconds and the displacement in the first 2 seconds:

θ_{2} = θ_{total} - θ_{1} = 8 α - 2 α = 6 α

Finally, the ratio $\frac{θ_{2}}{θ_{1}}$ is:

\frac{θ_{2}}{θ_{1}} = \frac{6 α}{2 α} = 3

💡 Teacher's Secret Hint

Remember that $θ_{2}$ refers to the displacement in the *second* time interval, not the total displacement up to that point.

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Physics Question 30 – JEE-MAIN 2026

Clue 1 of 3: Kinematics of Rotational Motion

🧠 Full Solution Path