Question

A body weighs $160N$ on the earth. Find its weight on another planet whose mass is $\frac{5}{2}$ times mass of earth and radius $\frac{4}{5}$ times that of earth.

• A. $125N$
• B. $625N$
• C. $225N$
• D. $25N$

Answer 1

The correct option is B $625N$

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 $\frac{5}{2}th$ of the earth= $\frac{5M}{2}$, Radius of the planet is $\frac{4}{5}$ of the earth= $\frac{4R}{5}$

So Weight of the body on the planet $w$'= $\frac{G\frac{5M}{2}m}{(\frac{4R}{5}{)}^2}$ ........(2)

Solving equation (1) and (2), $\Rightarrow w^{\prime }=625N$