Question

The mass of a planet is 4 times while its radius is 8 times that of the earth. If the weight of an object is 640 N on earth, what will be its weight on the planet?

• A. 40 N
• B. 80 N
• C. 160 N
• D. 120 N

Answer 1

Answer: (A)

40 N

Let mass of the earth is $M$ and radius of the earth is $R$.

So, acceleration due to gravity on earth's surface, $g=\frac{GM}{R^2}$ ......(1)

Then, mass of planet $=4M$

and radius of the planet $=8R$

So, acceleration due to gravity on planet's surface, $g_1=\frac{G\left(4M\right)}{(8R{)}^2}=\frac{GM}{16R^2}$

From equation (1),

$g_1=\frac{g}{16}$

we know, weight of body $=$ mass of body $\times$ acceleration due to gravity.

Here, mass of body is a constant term. it doesn't vary. so, weight of body depends on acceleration due to gravity.

So,

$\frac{W_e}{W_p}=\frac{g_e}{g_p}$

Here, $W_e$denotes weight of body on the earth, $W_p$ weight of body on the planet. similarly, $g_e$denotes acceleration due to gravity on the earth and $g_p$denotes acceleration due to gravity on the planet.

so, $\frac{640}{W_p}=\frac{g}{\left(g/16\right)}$

or, $\frac{640}{W_p}=16$

hence, $W_p=40N$