The ratio of the $K.E.$ required to be given to a satellite to escape Earth's gravitational field to the $K.E.$ required to be given so that the satellite moves in a circular orbit just above Earth's atmosphere is:

$A$ solid sphere of radius $R$ gravitationally attracts a particle of mass $m$ placed at a distance of $3R$ from its centre with a force $F_{1}$. Now,a spherical cavity of radius $\frac{R}{2}$ is made in the sphere (as shown in the figure) such that the cavity is tangent to the centre of the sphere and the outer surface. The force on the particle becomes $F_{2}$. The value of $F_{1} : F_{2}$ is:

If the radius of the Earth becomes $n$ times its present value,without any change in its mass,then the duration of the day becomes:

$A$ uniform sphere $A$ with radius $R$ exerts a gravitational force $F$ on a small particle $B$ situated at a distance $2R$ from the centre of the sphere. $A$ spherical portion of diameter $R$ is cut from the sphere $A$ such that its centre lies on the line connecting the centre of sphere $A$ and particle $B$. If $F^{\prime}$ is the new gravitational force between the remaining part of the sphere $A$ and the particle $B$, then find the correct relation between $F$ and $F^{\prime}$.

As we move towards the centre of the Sun,what happens to its physical properties?

Four particles,each of mass $M$ and equidistant from each other,move along a circle of radius $R$ under the action of their mutual gravitational attraction. The speed of each particle is