Question

A spot of light $S$ rotates in a horizontal plane with a constant angular velocity of $0.1\, rad / s$. The spot of light $P$ moves along the wall at a distance of $3\, m$ from $S.$ The velocity of spot $P$, where $\theta=45^{\circ}$, 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
$v=\frac{d x}{d t}=r \sec ^{2} \theta\left(\frac{d \theta}{d t}\right)$
where, $\frac{d \theta}{d t}=$ angular velocity of rotation of spot
$=\omega$
$\therefore v=\omega r \sec ^{2} \theta$
At $\phi=45^{\circ}$, so $\theta=45^{\circ}$
Hence, $v=0.1 \times 3 \times \sec ^{2} 45^{\circ}$
$=0.1 \times 3 \times 2=0.6\, m / s$