Question

Perfectly reflecting mirror of mass $M$ mounted on a spring constitutes a spring mass system of angular frequency $\Omega ,$ such that $\frac{4\pi M\Omega }{h}={10}^{34}{m}^{-3},$ where $h$ is planck constant, $N$ photons of wavelength $\lambda =8\pi \times {10}^{-6}\text{m}$ strikes the mirror simultaneously at normal incidence such that the mirror gets displaced by $1\mu m.$ If the value of $N$ is $x\times {10}^{-2},$ then the value of $x$ is

Answer 1

Momentum transferred on mirror $=\frac{2Nh}{\lambda }$
$\frac{2Nh}{\lambda }=M{V}_{meanposition}$
For SHM
$V_{meanposition}=\Omega A(\text{where},A=1\mu M)$

$\frac{2Nh}{\lambda }=M\Omega A(\text{where},\lambda =8\pi \times {10}^{-8})$
$N=\frac{M\Omega \left({10}^{-6}\right)\lambda }{2h}=\frac{M\Omega 8\pi \times {10}^{-6}\times {10}^{-6}}{2h}N=\frac{4\pi M\Omega }{h}\times {10}^{-12}={10}^{24}\times {10}^{-12}$
$N=1\times {10}^{-12}$
$x=1$