Gravitation Tes...

The distances from the centre of the earth, where the weight of a body is zero and one-fourth that of the weight of the body on the surface of the earth are (assume $R$ is the radius of the earth)

In a relation $\displaystyle \sqrt{\frac{2GM}{R}} \geq C$, G stands for universal gravitational constant, M for mass of a very very dense material, R for a small radius and C for velocity of light. Then,

If ${ g }$ is the acceleration due to gravity on the earth's surface, the change in the potential energy of an object of mass $m$ raised from the surface of the earth to a height equal to the radius $R$ of the earth is

Two equals masses each $m$ and $m$ are hung from a balance whose scale pans differ in vertical height by $'h'$. The error in weighing in terms of density of the earth $\rho$ is:

If $g$ is acceleration due to gravity on the earth's surface, the gain in the potential energy of an object of mass $m$ raised from the surface of earth to a height equal to the radius $R$ of the earth is

A body of mass ${ m }$ rises to a height ${ h }=\dfrac{R}{5}$ from the earth's surface where ${ R }$ is the earth's radius. If  $g$ is acceleration duem to gravity at the earth's surface, the increase in potential energy is

The value of ${ g }$ at a certain height ${ h }$ above the free surface of the earth is ${ x }/{ 4 }$ where ${ x }$ is the value of ${ g }$ at the surface of the earth. The height ${ h }$ is

The change in the value of $g$ at a height $h$ above the surface of earth is the same as at a depth $d$ below the earth. When both $d$ and $h$ are much smaller than the radius of earth, then which one of the following is correct?

If an artificial satellite is moving in a circular orbit around the earth with a speed equal to half the magnitude of the escape velocity from the earth, the height of the satellite above the surface of the earth is

The gravitational potential due to earth at infinite distance from it is zero. Let the gravitational potential at a point $P$ be $-{ 5 }{ J }{ kg }^{ -1 }$. Suppose, we arbitrarily assume the gravitational potential at infinity to be $+{ 10 }{ J }{ kg }^{ -1 }$, then the gravitational potential at $P$ will be