A perfectly reflecting body (sphere in shape) is placed on a path of parallel light beam of intensity $I$ shown in figure. One end of a spring is attached to the centre of the sphere and the other end to a rigid wall as shown in the figure. Sphere is in equilibrium. Spring constant of spring is $K$ . Then compression in spring is
(Radius of sphere is $R$ , $c$ is the velocity of light and neglect any thermal effect and friction )

\frac{2 I}{K c} π R^{2}

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\frac{I}{K c} π R^{2}

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\frac{4 I π R^{2}}{K c}

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\frac{I π R^{2}}{2 K c}

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Solution

The correct option is B $\frac{I}{K c} π R^{2}$
The force on the perfectly reflecting sphere is,

$F_{R} = \frac{I}{c} π R^{2}$

if $x$ is the compression in the spring, then force on the spring

$F_{s} = K x$

At equilibrium, $F_{s} = F_{R}$

$\Rightarrow K x = \frac{I}{c} π R^{2}$

$∴ x = \frac{I π R^{2}}{K C}$

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

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Q. A perfectly reflecting body (sphere in shape) is placed on a path of parallel light beam of intensity

I

shown in figure. One end of a spring is attached to the centre of the sphere and the other end to a rigid wall as shown in the figure. Sphere is in equilibrium. Spring constant of spring is

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(Radius of sphere is

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is the velocity of light and neglect any thermal effect and friction )

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