A spot light $S$ rotates in a horizontal plane with a constant angular velocity of $0.1 r a d / s$ . The spot of light $P$ moves along the wall at a distance $3 m$ . What is the velocity of the spot $P$ when $θ = 45^{o}$ ?

0.6 m / s

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0.5 m / s

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0.4 m / s

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0.3 m / s

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Solution

The correct option is A $0.6 m / s$
$Linear velocity, v = \frac{w r}{sin θ}$

If d is the distance from the spot light to wall

$r = \frac{d}{c o s θ}$

$= \frac{3}{cos (45^{\circ})}$

$velocity of the spot, v = \frac{l o r}{sin θ} = \frac{0.1 \times \frac{3}{cos 45^{\circ}}}{sin 45^{\circ}}$

$= 0.6 m s^{- 1}$

Suggest Corrections

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0.1 r a d / s

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Column I	Column II
(A) Velocity of spot $S$ in $m / s$ when it is closest to $L$ is	(p) $0.6$
(B) Acceleration of the spot in $m / s^{2}$ when $ϕ = 45^{o}$	(q) $0.3$
(C) Value of ratio of $ϕ$ in radians to $π$ radians when velocity of spot is $0.6 m / s$ is	(r) $0.25$
(D) Angular acceleration of the spot light $L$ when $ϕ = 30^{o}$	(s) $0$
	(t) $0.12$