Question

A body weighs $160N$ on the earth. Find its weight on another planet whose mass is $\frac{1}{4}th$ the mass of earth and radius $\frac{1}{3}rd$ that of the earth.

• A. $40N$
• B. $320N$
• C. $360N$
• D. $180N$

Answer 1

The correct option is C $360N$

We know the relation of gravity on any planet, $g=\frac{GM}{R^2}$

Where $G$ = Universal Gravitational Constant

$M$= Mass of the planet

$R$= Radius of the planet

Let assume mass of the body is $m$.

Weight of the body at the earth , $w=\frac{GMm}{R^2}=160N$ ......(1)

Given that Mass of the planet is $\frac{1}{4}th$ of the earth= $\frac{M}{4}$, Radius of the planet is $\frac{1}{3}rd$ of the earth= $\frac{R}{3}$

So Weight of the body on the planet, $w$'= $\frac{G\frac{M}{4}m}{(\frac{R}{3}{)}^2}$ ........(2)

Solving equation 1 and 2, $\Rightarrow w^{\prime }=360N$