Question

A planet reduces its radius by 1 % with its mass remaining same . How acceleration due to gravity varies ?​

Answer 1

Let the mass and radius of the earth be M and R respectively.

Acceleration due to gravity, g = GM/R^2

When the radius, R’ = R-R/100 = 99R/100 = 0.99R

So, the acceleration due to gravity, g’ = GM/(0.99R)^2

or, g’ = 1.02GM/R^2

Now, the change in acceleration due to gravity,

=g’ – g

=(1.02-1)GM/R^2

= (0.02)GM/R^2

Thus, the acceleration due to gravity increases by 2%.