Question

What will be the value of acceleration due to gravity on the surface of the earth if the radius of the earth suddenly decreases to 60% of its present value, keeping the mass of the earth unchanged?

(a) 9.81 m/s^2

(b) 5.89 m/s^2

(c) 16.35 m/s^2

(d) 27.25 m/s^2

This question was addressed to me in my homework.

My question is from Universal Law of Gravitation in portion Gravitation of Physics – Class 11

Answer 1

The correct option is (d) 27.25 m/s^2

For explanation I would say: From Newton’s law of gravitation, we have;

g = (G*M1)/R^2

Since the radius is reduced to 60% of its original value;

The new radius R’ = 0.6 x R

Therefore;

g’ = (G*M1)/(0.6*R) ^2

g’ = g/(0.6) ^2

= 9.81 / (0.6 x 0.6)

g’ = 27.25 m/s^2.