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A perfectly reflecting body in shape of a sphere of radius $R$ is placed on a path of parallel light beam of intensity I shown in figure. One end of a spring is attached to centre of sphere and the other end to a rigid wall as shown in figure. Assuming the sphere to be in equilibrium, the spring constant of spring to be $K$ , then compression in spring is
(Neglect any thermal effect and friction is absent)

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None of these

$\frac{π I R^{2}}{K c}$

$\frac{I K R^{2}}{c}$

$\frac{2 l R^{2}}{K c}$

answer is B.

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Detailed Solution

For a perfectly reflecting sphere of radius R, the effective area (A) for calculating the force due to reflected light is $A = {πR}^{2}$ .

From the force equilibrium of the sphere, assuming spring compression to be $x_{0}$ ,

$K x_{0} = \frac{I A}{c} = \frac{I (π R^{2})}{c} \Rightarrow x_{0} = \frac{π I R^{2}}{K c}$

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