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 $\theta_{1}$ and in the next 2 s it rotates through an angle $\theta_{2}$. The ratio $\frac{\theta_{2}}{\theta_{1}}$ is ______.

JEE Main · 2026 · 05 Apr 2026 · Shift 2 · Rotational Mechanics

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 ______.

(A)6
(B)3✓ Correct
(C)4
(D) $\frac{1}{3}$

Answer: (B)

Solution

Starting from rest with uniform angular acceleration

α

, the angle swept in time

t

θ = \frac{1}{2} α t^{2}

. In the first

2 s

θ_{1} = \frac{1}{2} α (2)^{2} = 2 α

. In the first

4 s

the total angle is

\frac{1}{2} α (4)^{2} = 8 α

, so the angle in the next

2 s

θ_{2} = 8 α - 2 α = 6 α

. The ratio is

\frac{θ _{2}}{θ _{1}} = \frac{6 α}{2 α} = 3

JEE Main · 2026 · 05 Apr 2026 · Shift 2 · Single correct option

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