Question

A $1{\text{MW/m}}^2$ continuously operating laser, is used as in "light rocket", to propel a $100\text{kg}$ spacecraft, through gravity free space. The cross-sectional area of the beam is $3{\text{m}}^2$. What is the acceleration of the spacecraft?

• A. $a={10}^{-6}{\text{m/s}}^2$
• B. $a={10}^{-4}{\text{m/s}}^2$
• C. $a={10}^{-10}{\text{m/s}}^2$
• D. $a={10}^{-2}{\text{m/s}}^2$

Answer 1

The correct option is B $a={10}^{-4}{\text{m/s}}^2$

The net force acting on the spacecraft is,
$F_{net}=F_T$
Here, $F_T$ is the thrust produced by the radiation pressure.

Now, $F_T=\frac{IA}{c}$, assuming complete absorption.

$\therefore ma=\frac{IA}{c}\Rightarrow a=\frac{IA}{mc}$

$a=\frac{{10}^6\times 3}{100\times 3\times {10}^8}$

$\therefore a={10}^{-4}{\text{m/s}}^2$

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