A body attains a height equal to the radius of the Earth when projected from Earth' surface. The velocity of the body with which it was projected is :-

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 the radius $R$ of Earth will be:-

A spherical cave of radius $\frac{R}{2}$ was carved out from a uniform sphere of radius $R$ and original mass $M$. The center of the cave is at $\frac{R}{2}$ from the center of the large sphere Point $P$ is at a distance $2R$ from the center of the large sphere and on the joint line of the two centers. The gravitational field strength $g$ at point $P$ is :-