A tunnel is dug along a diameter of the earth. If $M_e$ and $R_e$ are the mass and radius of the earth respectively. Then the force on a particle of mass $'m'$ placed in the tunnel at a distance $r$ from the centre is
$\frac{{G{M_e}m}}{{R_e^3}}.r$
$\frac{{G{M_e}}}{{R_e^3}}.\frac{m}{r}$
$\frac{{G{M_e}m}}{r}.R_e^3$
$\frac{{G{M_e}m}}{{R_e^2}}.r$
A geostationary satellite is orbiting the earth at a height of $6\,R$ above the surface of earth ($R$ is the radius of earth). The time period of another satellite at a height of $2.5\,R$ from the surface of the earth is :-
Three identical bodies of equal mass $M$ each are moving along a circle of radius $R$ under the action of their mutual gravitational attraction. The speed of each body is
The kinetic energy needed to project a body of mass $m$ from the earth's surface (radius $R$) to infinity is
What should be the angular speed of the earth, so that a body lying on the equator may appear weightlessness $(g = 10\,m/s^2, R = 6400\,km)$
Two masses $m_1$ and $m_2$ start to move towards each other due to mutual gravitational force. If distance covered by $m_1$ is $x$, then the distance covered by $m_2$ is