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A rectangular plate of mass m and area A is placed vertically on a smooth horizontal surface and connected to an ideal spring of stiffness constant k in relaxed position as shown. A parallel beam of light of intensity I is incident at an angle $θ$ to the normal to the plate, then choose the correct statement(s). (The plate is completely reflecting)

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Force on the plate due to beam of light, $F = \frac{2 I A \cos^{2} θ}{k c}$

Force on the plate due to parallel beam of light, $F = \frac{2 I A}{c}$

Plate oscillates with the period, $T = 2 π \sqrt{\frac{m}{k}}$

Amplitude of SHM, $A_{0} = \frac{2 I A \cos^{2} θ}{k c}$

answer is A, D.

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Detailed Solution

$T = 2 π \sqrt{\frac{m}{k}}$
Momentum of light between falling on the plate
Per second $= \frac{I A \cos^{2} θ}{c}$
$F = Δ p / \sec = = \frac{2 I A \cos^{2} θ}{c} F = k A_{0} A_{0} = \frac{F}{k} = \frac{2 I A \cos^{2} θ}{k c}$

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