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

$3$ identical point particles of mass $M$ move in such a way that the distance between particles is $d$ which remain constant. Only force is the gravitational force between particles. Then magnitude of relative velocity (in $\mathrm{m} {\mathrm{s}}^{-1}$) of one particle with respect to other particle will be : [Take $\sqrt{\frac{GM}{d}}=\sqrt{3} \mathrm{m} {\mathrm{s}}^{-1}$]

At what height above the earth's surface does the acceleration due to gravity fall to $1\%$ of its value at the earth's surface?

A planet has a mass $M_1$ and radius $R_1$. The value of acceleration due to gravity on its surface is $g_1$. There is another planet $2$, whose mass and radius both are two times that of the first planet. Which one of the following is the acceleration due to gravity on the surface of planet $2$?

Imagine a new planet having the same density as that of the earth but it is $3$ times bigger than the earth in size. If the acceleration due to gravity on the surface of the earth is $g$ and on the surface of the new planet is $g^{\text{'}}$, then

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

Gravitational acceleration on the surface of a planet is $\frac{\sqrt{6}}{11} g,$ where $g$ is the gravitational acceleration on the surface of the earth. The average mass density of the planet is $\frac{2}{3}$ times that of the earth. If the escape speed on the surface of the earth is taken to be $11km{s}^{-1},$ find the escape speed on the surface of the planet in $km{s}^{-1}.$

Which of the following graphs represent the time period of the planet moving around the sun? [$R$ is semi-major axis of the path.]

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,