Question

The weight of an object at earth's surface is $700\, g\, wt$. What will be its weight at the surface of a planet whose radius is $1 / 2$ and mass is $1 / 7$ of that of the earth ?

• A. 200 g wt.
• B. 400 g wt.
• C. 50 g wt.
• D. 300 g wt.

Answer 1

Answer: (B)

Weight at earth's surface $w=m g$
Acceleration due to gravity at earth's surface
$g=\frac{G M_{c}}{R_{e}^{2}}$
For planet, $g'=\frac{G M}{R^{2}}=\frac{G M_{c} / 7}{\left(R_{e} / 2\right)^{2}}$
$=\frac{4}{7} \frac{G m_{e}}{R_{e}^{2}}=\frac{4}{7} g$
$\therefore $ Weight at the surface of planet $=m g'$
$=m\left(\frac{4 g}{7}\right)$
$=\frac{4}{7} m g=\frac{4}{7} \times 700$
$=400\, g\, wt$