Q. If a planet of given density were made larger its force of attraction for an object on its surface would increase because of planet’s greater mass but would decease because of the greater distance from the object to the centre of the planet. Which effect predominate?
A) Increases in mass
B) Increase in radius
C) Both affect attraction equally
D) None of the above
Explanation
(a) Let $R$ be the original radius of a planet. Then attraction on a body of mass $m$ placed on its surface will be
$F = \frac{GM\ m}{R^{2}}$
If size of the planet is made double $ie,R^{'} = 2R,$ then mass of the planet becomes
$M^{'} = \frac{4}{3}\pi(2R)^{3}\rho = 8 \times \frac{3}{4}\pi R^{2}\rho = 8M$
New force $F^{'} = - \frac{GM^{'}m}{R^{'2}} = - \frac{G8M \times m}{(2R)^{2}} = 2F$
$ie,$ force of attraction increases due to the increase in mass of the planet
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.