Question

Let the radius of the earth be R. Now, assume that the earth shrunk by 20% but the mass is the same. What would be the new value of acceleration due to gravity at a distance R from the centre of the earth if the value at the same distance in the previous case was “g’”?

(a) g’

(b) 2g’

(c) 3g’

(d) 4g’

I had been asked this question by my college professor while I was bunking the class.

The above asked question is from Acceleration due to Gravity below and above the Surface of Earth topic in portion Gravitation of Physics – Class 11

Answer 1

The correct option is (a) g’

Easy explanation: The value of acceleration due to gravity before shrinking at a distance R from the centre of the earth, i.e., on the surface of the earth is;

g’ = (G*M)/R^2

Where; M = Mass of the earth

Now, the earth shrunk by 20%, however, the mass remains the same. This implies an increase in density.

The value of acceleration due to gravity from an object at a point outside the object is dependent only on the distance between the centre of gravity of the object and the distance between the point and the object. It is independent of density.

Hence, the new value of acceleration due to gravity at the same distance will remain unchanged, i.e., g’.