Light of intensity, $I$ is incident perpendicularly on a perfectly reflecting plate of area $A$ kept in a gravity-free space. If the photons strike the plate symmetrically and initially the spring was at its natural length, find the maximum compression in the springs.

\frac{2 I A}{3 K c}

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\frac{2 I A}{K c}

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\frac{4 I A}{3 K c}

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\frac{I A}{3 K c}

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Solution

The correct option is A $\frac{2 I A}{3 K c}$
As we know, for a perfectly reflecting plate, the force exerted on the plate by beam

$F = \frac{2 I A}{c}$

Force, acting on the spring, $F_{s p r i n g} = K_{e q v} x$

Where, $x$ is the maximum compression.

$F = F_{s p r i n g}$

$\Rightarrow \frac{2 I A}{c} = K_{e q v} x$

$\Rightarrow \frac{2 I A}{c} = (3 K) x$

$∴ x = \frac{2 I A}{3 K c}$

Hence, $(A)$ is the correct answer.

Why this question?

Keynote: This type of multiconcpets question are frequently asked in JEE Advance papers.

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Light of intensity, I is incident perpendicularly on a perfectly reflecting plate of area A kept in a gravity-free space. If the photons strike the plate symmetrically and initially the spring was at its natural length, find the maximum compression in the springs.

Light of intensity, $I$ is incident perpendicularly on a perfectly reflecting plate of area $A$ kept in a gravity-free space. If the photons strike the plate symmetrically and initially the spring was at its natural length, find the maximum compression in the springs.