Question

A spot of light $S$ rotates in a horizontal plane with a constant angular velocity of $0.1rad/s$. The spot of light $P$ moves along the wall at a distance of $3m$ from $S.$ The velocity of spot $P$, where $\theta =45^{\circ }$, is

• A. 0.5 m/s
• B. 0.6 m/s
• C. 0.7 m/s
• D. 0.8 m/s

Answer 1

Answer: (B)

The situation is shown in figure.

From figure,
$x=r\tan \theta$
$\therefore$ Velocity of $P$ is
$v=\frac{dx}{dt}=r{\sec }^2\theta \left(\frac{d\theta }{dt}\right)$
where, $\frac{d\theta }{dt}=$ angular velocity of rotation of spot
$=\omega$
$\therefore v=\omega r{\sec }^2\theta$
At $\varphi =45^{\circ }$, so $\theta =45^{\circ }$
Hence, $v=0.1\times 3\times {\sec }^{2}45^{\circ }$
$=0.1\times 3\times 2=0.6m/s$