Embibe Experts Solutions for Chapter: Gravitation, Exercise 2: Level 2

Let $V$ and $E$ be the gravitational potential and gravitational field at a distance $r$ from the centre of a uniform spherical shell. Consider the following two statements :
(A) The plot of $V$ against $r$ is discontinuous.
(B) The plot of $E$ against $r$ is discontinuous.

The maximum height reached by a rocket fired with a speed equal to $50\%$ of the escape velocity from the earth's surface is,

The mass density of a planet of radius $R$ varies with the distance $r$ from its centre as $\rho \left(r\right)={\rho }_0\left(1-\frac{r^2}{R^2}\right)$, then the gravitational field is maximum at:

A body is projected vertically upwards from earth's surface with velocity $2v_e,$ where $v_{\mathit{e}}$ is escape velocity from earth's surface. The velocity when body escapes the gravitational pull is

If a projectile has a velocity greater than the escape velocity, which trajectory will it follow?

A satellite is launched into a circular orbit of radius $R$ around the earth. A second satellite is launched into an orbit of radius $1.02R$. The period of second satellite is larger than the first one by approximately,

A body is dropped by a satellite in its geostationary orbit:

A remote - sensing satellite of earth revolves in a circular orbit at a height of $0.25\times {10}^6 \mathrm{m}$ above the surface of earth. If earth's radius is $6.38\times {10}^6 \mathrm{m}$ and $g=9.8 \mathrm{m} {\mathrm{s}}^{-2},$ then the orbital speed of the satellite is