The masses $m$ in fig. $(A)$ and $(B)$ are identical. The gravitational potential energy in the two cases are $U_A$ and $U_B$. Then
$U_A = U_B \neq 0$
$U_A < U_B$
$U_A > U_B$
$U_A = U_B = 0$
The speed of a satellite in a circular orbit of radius $R_0$ around the earth is $v_0$. Another satellite is in an elliptic orbit around the earth. If the minimum and maximum speeds of the second satellite are $\alpha v_0$ and $\beta v_0$ respectively, then its time period is
A satellite of mass $m$ is orbiting the earth $($of radius $R)$ at a height $h$ from its surface. The total energy of the satellite in terms of $g_0$, the value of acceleration due to gravity at the earth's surface, is
A rocket is fired vertically with a speed of $5\; km s^{-1}$ from the earth’s surface. How far from the earth does the rocket go before returning to the earth ? Mass of the earth $=6.0 \times 10^{24} \;kg ;$ mean radius of the earth $=6.4 \times 10^{6} \;m ; G=6.67 \times 10^{-11} \;N m ^{2} kg ^{2}$
A body of mass $'m' $ is taken from the earth's surface to the height equal to twice the radius $(R)$ of the earth. The change in potential energy of body will be
Two masses $m_1\, \& m_2$ are initially at rest and are separated by a very large distance. If the masses approach each other subsequently, due to gravitational attraction between them, their relative velocity of approach at a separation distance of $d$ is :