A body of mass $m$ falls from a height $R$ above the surface of the earth, where $R$ is the radius of the earth. What is the velocity attained by the body on reaching the ground? (Acceleration due to gravity on the surface of the earth is $g$)
$gR$
$\sqrt {gR} $
$\sqrt {g/R} $
$g/R$
A satellite $S$ is moving in an elliptical orbit around the earth. The mass of the satellite is very small compared to the mass of the earth. Then
A thin rod of length $L$ is bent to form a semicircle. The mass of rod is $M.$ What will be the gravitational potential at the centre of the circle?
A particle is kept at rest at a distance $'R'$ from the surface of earth (of radius $R$). The minimum speed with which it should be projected so that it does not return is
Figure shows the orbit of a planet $P$ round the sun $S.$ $AB$ and $CD$ are the minor and major axes of the ellipse.
If $t_1$ is the time taken by the planet to travel along $ACB$ and $t_2$ the time along $BDA,$ then
If the gravitational acceleration at surface of Earth is $g$, then increase in potential energy in lifting an object of mass $m$ to a height equal to half of radius of earth from surface will be