Embibe Experts Solutions for Chapter: Gravitation, Exercise 3: Exercise-3

The figure shows elliptical orbit of a planet $m$ about the sun $S$. The shaded area $SCD$ is twice the shaded area $SAB$. If $t_1$ is the time for the planet to move from $C$ to $D$ and $t_2$ is the time to move from $A$ to $B$, then:

The dependence of acceleration due to gravity $g$ on the distance $r$ from the centre of the earth, assumed to be a sphere of radius $R$ of uniform density is as shown in figures below. The correct figure is.

Which one of the following plots represents the variation of the gravitational field on a particle with distance $r$ due to a thin spherical shell of radius $R$ ? ($r$ is measured from the centre of the spherical shell)

Starting from the centre of the earth having radius $r$, the variation of $g$ (acceleration due to gravity) is shown by

The kinetic energies of a planet in an elliptical orbit about the Sun, at positions $A, B$ and $C$ are $K_A, K_B$ and $K_C$ respectively. $AC$ is the major axis and $SB$ is perpendicular to $AB$ at the position of the Sun $S$ as shown in the figure. Then

Two bodies of masses $M$ and $4M$ Are placed at a distance $r$. The gravitational potential at a point on the line joining them where the gravitational field is zero is.

From a solid sphere of mass $M$ and radius $R$, a spherical portion of radius $\frac{R}{2}$ is removed, as shown in the figure. Taking gravitational potential $V=0$ at $r=\infty$, the potential at the centre of the cavity thus formed is:($G=$ gravitational constant)

A straight rod of length $L$ extends from $x=a$ to $x=L+a$. The gravitational force it exerts on a point mass $m$ at $x=0$, if the mass per unit length of the rod is $A+B{x}^2$, is given by