Umakant Kondapure, Collin Fernandes, Nipun Bhatia, Vikram Bathula and, Ketki Deshpande Solutions for Chapter: Gravitation, Exercise 2: Critical Thinking

At a given place where the acceleration due to gravity is $g$ $\mathrm{m} {\mathrm{s}}^{-2}$, a sphere of lead of density $d$ $\mathrm{kg} {\mathrm{m}}^{-3}$ is gently released in a column of liquid of density $\rho$ $\mathrm{kg} {\mathrm{m}}^{-3}.$ If $d>\rho ,$ the sphere will

What should be the velocity of the earth due to rotation about its own axis so that the weight at the equator becomes $\frac{3}{5}$ of initial value? Radius of earth on the equator is $6400 \mathrm{km}$.

Imagine a light planet revolving around a very massive star in a circular orbit of radius $r$ with period $T$. If the gravitational force of attraction between planet and star is proportional to $R^{-\frac{3}{2}},$ then $T^2$ is proportional to

Assertion: The artificial satellite does not have any fuel but even then it remains orbiting around the earth.

Reason: The necessary centripetal force required to move the satellite in an orbit around the earth is provided by the gravitational force of attraction between the satellite and the earth.

Assertion: When an object is weighed with a physical balance, then its mass will be the same both at the pole and at the equator.

Reason: When a body is weighed with a spring balance, then its weight will be maximum at the pole.

A satellite is placed in a circular orbit about Earth with a radius equal to half the radius of the moon's orbit. The period of rotation of the satellite is $n$ times that of the lunar month (lunar month is the period of revolution of the moon). The value of $n$ is

A diametrical tunnel is dug across the Earth. A ball is dropped into the tunnel from one side. The velocity of the ball, when it reaches the centre of the Earth is (Given: gravitational potential at the centre of Earth $=-\frac{3}{2}\frac{\mathit{G}\mathit{M}}{\mathit{R}}$)

The acceleration due to gravity at a height ${\left(\frac{1}{20}\right)}^{th}$ of the radius of the earth above the earth surface is $9 \mathrm{m} {\mathrm{s}}^{-2}$. Its value at a point at an equal distance below the surface of the earth in $\mathrm{m} {\mathrm{s}}^{-2}$ is about?  (Take the value of $g$ at the earth's surface as $10 \mathrm{m} {\mathrm{s}}^{-2}$)