An object is taken to height $2 R$ above the surface of earth, the increase in potential energy is $[R$ is radius of earth]
$\frac{m g R}{2}$
$\frac{m g R}{3}$
$\frac{2 m g R}{3}$
$2 m g R$
A satellite is launched into a circular orbit of radius $R$ around earth, while a second satellite is launched into a circular orbit of radius $1.02\, {R}$. The percentage difference in the time periods of the two satellites is -
If the distance between centres of earth and moon is $D$ and the mass of earth is $81\, times$ the mass of moon, then at what distance from centre of earth the gravitational force will be zero
A satellite of mass $m$ is in a circular orbit of radius $2R_E$ about the earth. The energy required to transfer it to a circular orbit of radius $4R_E$ is (where $M_E$ and $R_E$ is the mass and radius of the earth respectively)
Suppose the gravitational force varies inversely as the $n^{th}$ power of the distance. Then, the time period of a planet in circular orbit of radius $R$ around the sun will be proportional to
Which of the following graph represents the variations of acceleration due to gravity $(g)$ with distance $r$ from the centre of earth?