Question

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 )

• A. $\frac{2I}{Kc}\pi R^2$
• B. $\frac{I}{Kc}\pi R^2$
• C. $\frac{4I\pi R^2}{Kc}$
• D. $\frac{I\pi R^2}{2Kc}$

Answer 1

The correct option is B $\frac{I}{Kc}\pi R^2$

The force on the perfectly reflecting sphere is,

$F_R=\frac{I}{c}\pi R^2$

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

$F_s=Kx$

At equilibrium, $F_s=F_R$

$\Rightarrow Kx=\frac{I}{c}\pi R^2$

$\therefore x=\frac{I\pi R^2}{KC}$

Hence, $\left(B\right)$ is the correct answer.