Rotational Motion

JEE Main level, single correct, medium

139 of 280

Question 139 of 280

A wheel initially at rest is subjected to a uniform angular acceleration about its axis. In the first 2 s2\text{ s} it rotates through an angle θ1\theta_1 and in the next 2 s2\text{ s} it rotates through an angle θ2\theta_2. The ratio θ2θ1\dfrac{\theta_2}{\theta_1} is _______.

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Answer: (B) 33

Using the equation of rotational kinematics θ=ω0t+12αt2\theta = \omega_0 t + \dfrac{1}{2} \alpha t^2.

Since the wheel is initially at rest, ω0=0\omega_0 = 0.

Angle rotated in the first 2 s2\text{ s}:

θ1=12α(2)2=2α\theta_1 = \dfrac{1}{2} \alpha (2)^2 = 2\alpha

Angle rotated in the first 4 s4\text{ s}:

θtotal=12α(4)2=8α\theta_{total} = \dfrac{1}{2} \alpha (4)^2 = 8\alpha

Angle rotated in the next 2 s2\text{ s}:

θ2=θtotal−θ1=8α−2α=6α\theta_2 = \theta_{total} - \theta_1 = 8\alpha - 2\alpha = 6\alpha

The ratio is:

θ2θ1=6α2α=3\dfrac{\theta_2}{\theta_1} = \dfrac{6\alpha}{2\alpha} = 3

Answer: 33

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