Question

Distance between two masses is reduced to half. What is The % change in their mutual gravitational force?

Answer 1

the force is quadrupled. hence the Percentage change is 300% increased

Answer 2

Given:

Two masses under mutual gravitational force separated by some distance

To Find:

The percentage change in their mutual gravitational force if the distance is reduced to half

Solution:

The gravitational force F between two bodies of masses M and m kept at a distance d from each other is given by

F = G m M / d²       - (1)

Where,

G is the gravitational constant and has the value 6.67430 × 10⁻¹¹ m³ kg⁻¹ s⁻²

Given that the distance is reduced to half then,

d → d / 2

The new gravitational force F' = $\frac{GmM}{(\frac{d}{2} )^2}$       - (2)

= 4 G m M / d

From equations 1 and 2, we can say that

F' = 4 X F

The percentage change = (New Value - Initial Value) X 100/ Initial Value

= (F' - F )X 100/ F

= (4F - F) X100  / F

= 300%

Hence, the percentage increase in their mutual gravitational force is 300%.