A particle is dropped on Earth from height $R$ (radius of Earth) and it bounces back to a height $R/2$ the coefficient of restitution for collision is (ignore air resistance and rotation of Earth)
$\frac{2}{3}$
$\sqrt {\frac{2}{3}} $
$\sqrt {\frac{1}{3}} $
$\sqrt {\frac{1}{2}} $
A body weighs $63\; N$ on the surface of the earth. What is the gravitational force (in $N$) on it due to the earth at a height equal to half the radius of the earth ?
What should be the angular speed with which the earth have to rotate on its axis so that a person on the equator would weigh $\frac{3}{5}$ th as much as present?
The acceleration due to gravity on the surface of earth is $g$. If the diameter of earth reduces to half of its original value and mass remains constant, then acceleration due to gravity on the surface of earth would be :
The ratio of the radius of the earth to that of the moon is $10$. The ratio of acceleration due to gravity on the earth and on the moon is $6$. The ratio of the escape velocity from the earth's surface to that from the moon is
Given below are two statements :
Statement $I$ : The law of gravitation holds good for any pair of bodies in the universe.
Statement $II$ : The weight of any person becomes zero when the person is at the centre of the earth. In the light of the above statements, choose the correct answer from the options given below.