Question

A small laser emits light at power $5\text{mW}$ and wavelength $633\text{nm}$. The laser beam is focused (narrowed) until its diameter matches the $1266\text{nm}$ diameter of a sphere placed in its path. The sphere is perfectly absorbing and has density $5\times {10}^3{\text{kg/m}}^3$. What is the magnitude of the acceleration that force alone would give the sphere ?

• A. $300{\text{m/s}}^2$
• B. $3434{\text{m/s}}^2$
• C. $3344{\text{m/s}}^2$
• D. $3144{\text{m/s}}^2$

Answer 1

The correct option is D $3144{\text{m/s}}^2$

Given:
$\lambda =633\text{nm};d=1266\text{nm}$
$\rho =5\times {10}^3{\text{kg/m}}^3$
$\text{Power}=5\times {10}^{-3}\text{W}$

Since, sphere is perfectly absorbing, so force exerted on the sphere will be

$F=\frac{IA}{c}=\frac{\text{Power}}{c}=\frac{5\times {10}^{-3}}{3\times {10}^8}$

$F=1.67\times {10}^{-11}\text{N}$

Mass of sphere,
$m=\rho \times \frac{\pi d^3}{6}=5\times {10}^3\times \frac{\pi }{6}\times (1266\times {10}^{-9}{)}^3$

$m=5.312\times {10}^{-15}\text{kg}$

Therefore, acceleration of the sphere due to incident rays will be,

$a=\frac{F}{m}=\frac{1.67\times {10}^{-11}}{5.312\times {10}^{-15}}=3144{\text{m/s}}^2$

Hence, option $\left(\text{D}\right)$ is correct.