Question

A body weighs 700 N on the surface of the earth. What is its weight on the surface of a planet whose mass is${\frac{1}{7}}^{th}$ of that of earth and radius is$\frac{1}{2}$ times of earth?

• A. 400 N
• B. 300 N
• C. 700 N
• D. 500 N

Answer 1

The correct option is A 400 N

$W_{earth}=700N=m{g}_{earth}$
$g_{planet}=\frac{G{M}_{planet}}{R_{planet}^2}=\frac{G\left(\frac{1}{7}{M}_{earth}\right)}{(\frac{1}{2}{R}_{earth}{)}^2}$
$=\frac{4G{M}_{earth}}{7(R_{earth}{)}^2}=\frac{4}{7}{g}_{earth}$
$W_{planet}=m{g}_{planet}$
$m\times \frac{4}{7}\times g_{earth}N$
$=\frac{4}{7}\times 700N=400N$