Question

suppose the earth shrinks such that its radius decreases to half of present value what will be acceleration due to gravity on the surface of the earth

Answer 1

We know,

Gravitational Constant (G) = 6.67× $10^{-11}$

Mass of Earth (M) = 6×$10^{24}$ kg

Radius of Earth (R) = 6400 km

New Radius (R') = 6400000/2 m = 3200000 m

Now,

When earth shrinks to half its radius then new acceleration due to gravity is

g' = $\frac{GM}{R'^2}$

Putting the values and solving it. We get,

g' = 39.0820 m/s^2