Question

Spotlight $S$ rotates in a horizontal plane with a constant angular velocity of $0.1rads^{- 1}$ . The spot of light $P$ moves along the wall at a distance of $3m$ . The velocity of the spot $P$ when $\theta =45^\circ $ (see. fig.) is

• A. $0.6 \, m \, s^{- 1}$
• B. $0.2ms^{- 1}$
• C. $0.3 \, m \, s^{- 1}$
• D. $0.1ms^{- 1}$

Answer 1

Answer: (A)

$\text{tan} \theta = \frac{\text{SM}}{\text{PM}}$
$\therefore \text{PM}=\frac{\text{SM}}{\text{tan} \theta }=3cot\theta $ $v=3\left|cosec^{2} \theta \right|\frac{d \theta }{d t}$ For $\theta =45^\circ $ $v=rω=3\times 2\times 0.1=0.6 \, m \, s^{- 1}$