Question

A wheel initially at rest, is rotated with a uniform angular acceleration. The wheel rotates through an angle $\theta_{1}$ in first one second and through an additional angle $\theta_{2}$ in the next one second. The ratio $\theta_{2} / \theta_{1}$ is :

• A. 4
• B. 2
• C. 3
• D. 1

Answer 1

Answer: (C)

Angle of rotation in 1 sec is
$\theta_{1} =\frac{1}{2} \alpha(1)^{2} $
$\theta_{1} =\frac{\alpha}{2}$
$\alpha =2 \theta_{1}\,\,\,...(1)$
$\Rightarrow \theta_{1}+\theta_{2}=\frac{1}{2} \alpha(2)^{2}$
$\Rightarrow \theta_{1}+\theta_{2}=\frac{1}{2}\left(2 \theta_{1}\right)(4)$
$\Rightarrow \theta_{1}+\theta_{2}=4 \theta_{1}$
$3 \theta_{1}=\theta_{2}$
$\Rightarrow \frac{\theta_{2}}{\theta_{1}}=3$