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?
(1) 40 N (2) 80 N
(3) 160 N (4) 120 N

Answer 1

answer : option (1) 40N

explanation : Let mass of the earth is M and radius of the earth is R.

so, acceleration due to gravity on earth's surface, g = GM/R² ......(1)

Then, mass of planet = 4M

and radius of the planet = 8R

so, acceleration due to gravity on planet's surface, g' = G(4M)/(8R)²

= GM/16R²

from equation (1),

g' = g/16

we know, weight of body = mass of body × 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, 640/$W_p$ = g/(g/16)

or, 640/$W_p$ = 16

hence, $W_p$ = 40N

Answer 2

Option A is correct.

40 N.