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 $3$m from S. The velocity of spot P, where $\theta ={45}^o$, is?

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

Answer 1

The correct option is B $0.6m/s$

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