Assume that a tunnel is dug through earth from North pole to south pole and that the earth is a non-rotating, uniform sphere of density $\rho $. The gravitational force on a particle of mass $m$ dropped into the tunnel when it reaches a distance $r$ from the centre of earth is
$\left( {\frac{3}{{4\pi }}\,mG\rho } \right)r$
$\left( {\frac{{4\pi }}{3}\,mG\rho } \right)r$
$\left( {\frac{{4\pi }}{3}\,mG\rho } \right)r^2$
$\left( {\frac{{4\pi }}{3}\,{m^2}G\rho } \right)r$
The potential energy of a satellite of mass $m$ and revolving at a height $R_e$ above the surface of earth where $R_e =$ radius of earth, is
Two particles of equal mass $'m'$ go around a circle of radius $R$ under the action of their mutual gravitational attraction. The speed of each particle with respect to their centre of mass is
Which graph correctly presents the variation of acceleration due to gravity with the distance from the centre of the earth (radius of the earth $= R_E$ )?
At what height above the earth's surface is the value of $'g'$ is same as in a $200\, km$ deep mine ........ $km$
A satellite in force free space sweeps stationary interplanetary dust at a rate of $\frac{d M}{d t}=\alpha v$ where $M$ is mass and $v$ is the speed of satellite and $\alpha$ is a constant. The acceleration of satellite is