Question

If the diameter of the earth becomes half of its original value, then mass becomes 1/8 of its original value. Find the acceleration due to gravity of this part.

Answer 1

Explanation:

Since we know that the formula for acceleration due to gravity is

$g = \dfrac{GM}{R^{2} }$................(1)

Where G =gravitaional constant,M=mass of the earth and R =radius of the earth.

Since it is given that the diameter of the earth becomes half of its original value, and mass becomes 1/8 of its original value.

So, acceleration due to gravity becomes,

$g' = \dfrac{GM}{2R^{2} }$..................(2)

From (1) and (2) we get,

The acceleration due to gravity becomes $\dfrac{1}{2}th$ of the original value.