Question

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

• A. 0.3 ms
• B. 0.6 ms
• C. 0.8 ms
• D. 1.2 ms

Answer 1

The correct option is B 0.6 ms

Linear Velocity of rotating object $\nu =\omega r/sin\theta$

$\omega =$ angular velocity $=0.1rad/s$

$r-$ distance of object from centre.

angle $=45°$

$r=d/cos\theta$ [ where d is the distance from the spot light to wall] $=3/cos45°$

Velocity$=\nu =\omega r/sin\theta$

$=\left[0.1x3/cos45°\right]/sin45°$

$=0.1x3/sin45°cos45°$

$=0.3/\left[1\surd 2x1/2\right]$

$=2x0.3$

$=0.6m/s$

$\therefore$The velocity of the spot P is $0.6m/s$

Hence, the option $B$ is the correct answer.