Question 21: Gravitation

Question

If the radius of earth were to shrink by two percent, its mass remaining the same, the acceleration due to gravity on the earth's surface would

Accepted Answer

The surface gravity is given by
$$g=\frac{GM}{R^2}\,. $$
If the radius shrinks by 2%, then
$$R_{\rm new}=0.98\,R\,, $$
so
$$g_{\rm new}=\frac{GM}{(0.98\,R)^2} =\frac{GM}{R^2}\cdot\frac{1}{0.98^2} \approx g\cdot\frac{1}{0.9604} \approx1.0412\,g\,. $$
ThatÃ¢ÂÂs about a 4 % increase.
Answer: Option C (Increase by 4 %).

Answer

Decrease by $4 \%$

Answer

Increase by $1 \%$

Answer

Increase by $4 \%$

Answer

Increase by $2 \%$

Gravitation

If the radius of earth were to shrink by two percent, its mass remaining the same, the acceleration due to gravity on the earth's surface would

Choose the correct answer: