Embibe Experts Solutions for Chapter: Gravitation, Exercise 1: Exercise-1

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:-

The intensity of gravitational field at a point situated at a distance $8000 \mathrm{km}$ from the centre of Earth is$6.0$ newton$/\mathrm{kg}$The gravitational potential at that point in newton $-$ meter$/\mathrm{kg}$ 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 :-

A satellite of mass $\mathrm{m}$ is at a distance a from a star of mass $\mathrm{M}$. The speed of satellite is $u$. Suppose the law of universal gravity is $F=-\mathrm{G}\frac{\mathrm{Mm}}{r^{2.1}}$ instead of $F=-\mathrm{G}\frac{\mathrm{Mm}}{r^2}$, find the speed of the satellite when it is at a distance b from the star.

Escape velocity of a body from the surface of Earth is $11.2 \mathrm{km} {\mathrm{s}}^{-1}$. from the Earth surface. If the mass of Earth becomes double of its present mass and radius becomes half of its present radius, then escape velocity will become 

A body of mass $m$ is situated at distance $4R_e$ above the earth's surface, where $R_{\mathit{e}}$ is the radius of earth how much minimum energy be given to the body so that it may escape :-

A hollow spherical shell is compressed to half its radius. The gravitational potential at the centre