Physics · Gravitation

the formula for gravitational constant “g” is:

                        g=GM/R² (1)

Where G is universal gravitational constant 

            M is mass of the earth 

            R is the radius of the earth.

The new value of "g" is now obtained from equation(1) by substituting R'=R2as follows: 

                        g'=GM/R²/4

                        g'=4GM/R²

                        g'=4g

So new gravitational acceleration g' is four times its initial value.

The right response is thus option A, which states that if the earth's radius were cut in half but its mass remained constant, the acceleration caused by gravity would increase by four times.

This is the correct answer. If the radius is halved and the mass remains the same, the gravitational acceleration increases fourfold.

This option suggests that the gravitational acceleration would only double, which is incorrect. A halving of the radius leads to a quadrupling of 'g', not a doubling.

This option implies that the gravitational acceleration decreases, which is incorrect. The acceleration actually increases when the radius is decreased while mass remains unchanged.

This option suggests the gravitational acceleration is halved, which is incorrect. Reducing the radius results in an increase, not a decrease, in gravitational acceleration.