B M Sharma Solutions for Chapter: Gravitation, Exercise 3: CONCEPT APPLICATION EXERCISE

Where will you weigh more and why:
$2\mathrm{k}\mathrm{m}$ above the surface of earth or
$2\mathrm{}\mathrm{k}\mathrm{m}$ helow the surface of earth?

Find the maximum change in reading of a spring balance if a block of mass $m$ is brought from pole to equator.

Find the height above the earth's surface, where the value of acceleration due to gravity is ${\left(3/4\right)}^{\mathrm{t}\mathrm{h}}$ the value on the surface, (take the radius of earth as $R$).

Find the percentage change in the acceleration due to gravity when a small body is taken to an altitude $\frac{R}{100}$.

The value of $\text{'}g\text{'}$ at a depth $d$, is two-third the value that on the earth's surface. Find $d$ in terms of radius of earth $R$.

The distance between earth and moon is $3.8\times {10}^5\mathrm{k}\mathrm{m}$ and the mass of earth is $81$ times the mass of the moon. Find the position of a point on the line joining the centres of earth and moon, where the gravitational field is zero. What would be the value of gravitational field there due to the earth and moon separately?
Given, radius of the earth $=6.4\times {10}^6\mathrm{}\mathrm{m}$.

A uniform solid sphere of mass $M$ and radius $a$ is surrounded symmetrically by a uniform thin spherical shell of equal mass and radius $2a$. Find the gravitational field at a distance
$3a/2$ from the centre

$h_1=\frac{R}{2}$. From the surface of the earth acceleration due to gravity is $g_1$. Its value changes by $∆g_1$ when one moves down further by $1\mathrm{}\mathrm{k}\mathrm{m}$. At a height $h_2$ above the surface of the earth acceleration due to gravity is $g_2$. Its value changes by $∆g_2$ when one moves up further by $1\mathrm{}\mathrm{k}\mathrm{m}$. If $∆g_1=∆g_2$, find $h_2$. Assume the earth to be a uniform sphere of radius $R$.