Embibe Experts Solutions for Chapter: Gravitation, Exercise 1: JEE Main - 1 September 2021 Shift 2

The time period of a satellite of earth is $24$ hours. If the separation between the earth and the satellite is decreased to one fourth of the previous value, then its new time period will become.

If the gravitational field in the space is given as $\left(-\frac{K}{r^2}\right)$. Taking the reference point to be at $r=2 \mathrm{cm}$ with gravitational potential $V=10 \mathrm{J} {\mathrm{kg}}^{-1}$. Find the gravitational potentials at $r=3 \mathrm{cm}$ in SI unit (Given, that $K=6 \mathrm{J} \mathrm{cm} {\mathrm{kg}}^{-1}$)

An object is allowed to fall from a height $R$ above the earth, where $R$ is the radius of earth. Its velocity when it strikes the earth’s surface, ignoring air resistance, will be :

At a certain depth $d$ below surface of earth, value of acceleration due to gravity becomes four times that of its value at a height $3R$ above earth surface. Where $R$ is Radius of earth (Take $R = 6400 \mathrm{km}$). The depth $d$ is equal to

A body weight $W$, is projected vertically upwards from earth's surface to reach a height above the earth which is equal to nine times the radius of earth. The weight of the body at that height will be:

Given below are two statements :

Statement-I: Acceleration due to gravity is different at different places on the surface of earth.

Statement-II: Acceleration due to gravity increases as we go down below the earth's surface.

In the light of the above statements, choose the correct answer from the options given below

If earth has a mass nine times and radius twice to the of a planet $P$. Then $\frac{v_e}{3}\sqrt{x}m{s}^{-1}$ will be the minimum velocity required by a rocket to pull out of gravitational force of $P$, where ve is escape velocity on earth. The value of $x$ is

The escape velocities of two planets $A and B$ are in the ratio $1 : 2$. If the ratio of their radii respectively is $1 : 3$, then the ratio of acceleration due to gravity of planet $A$ to the acceleration of gravity of planet $B$ will be: