Question

If the radius of the earth is reduced to half of its present value, with no change in the mass, the acceleration due to gravity will be:

• A. Doubled to that of its original value
• B. Four times that of its original value
• C. Remains same
• D. Reduced to half of its original value

Answer 1

The correct option is B Four times that of its original value

The formula for the acceleration due to gravity $\left(g\right)$ is given as $g=\frac{GM}{R^2}$ ...........(1)

Where $G$ is universal gravitational constant and $M$ is mass of the earth with $R$ as the radius of the earth.

Now $replacing$ $R$ by $R/2$ in the equation-1

we get the new value of $g$ as $g_{new}=\frac{GM}{R^2/4}=4\frac{GM}{R^2}$

Which is $four$ times of its original value.