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
$\frac{{mgR}}{2}$
$\frac{{2mgR}}{3}$
$\frac{{mgR}}{4}$
$\frac{{mgR}}{3}$
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
A planet orbits the sun in an elliptical path as shown in the figure. Let $v_P$ and $v_A$ be speed of the planet when at perihelion and aphelion respectively. Which of the following relations is correct ?
A skylab of mass $m\,kg$ is first launched from the surface of the earth in a circular orbit of radius $2R$ (from the centre of the earth) and then it is shifted from this circular orbit to another circular orbit of radius $3R$ . The minimum energy required to shift the lab from first orbit to the second orbit are
The orbital angular momentum of a satellite revolving at a distance $r$ from the centre is $L.$ If the distance is increased to $4r$ then the new angular momentum will be
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 $g$)