Dependence of acceleration due to gravity g on distance r from centre of earth assumed to be a spher

English

Gujarati

Hindi

7.Gravitation

normal

The dependence of acceleration due to gravity $g$ on the distance $r$ from the centre of the earth assumed to be a sphere of radius $R$ of uniform density is as shown figure below

The correct figure is

A

$(i)$

B

$(ii)$

C

$(iii)$

D

$(iv)$

Solution

The acceleration due to gravity at a depth d below surface of earth is

$g^{\prime}=\frac{G M}{R^{2}}\left(1-\frac{d}{R}\right)=g\left(1-\frac{d}{R}\right)$

$g^{\prime}=0$ at $d=R$

i.e., acceleration due to gravity is zero at the centre of earth.

Thus, the variation in value $g$ with $r$ is for, $r>R$

$g^{\prime}=\frac{g}{\left(1+\frac{h}{R}\right)^{2}}=\frac{g R^{2}}{r^{2}} \Rightarrow g^{\prime} \propto \frac{1}{r^{2}}$

Here, $R+h=r$

For $\quad r$

Here, $R-d=r \Rightarrow g^{\prime} \propto r$

Therefore, the variation of $g$ with distance from centre of the earth will be as shown in the figure.

Standard 11

Physics

Share

Similar Questions

$Assertion$ : The escape speed does not depend on the direction in which the projectile is fired.
$Reason$ : Attaining the escape speed is easier if a projectile is fired in the direction the launch site is moving as the earth rotates about its axis.

normal

A satellite $S$ moves around a planet $P$ in an elliptical orbit as shown in figure. The ratio of the speed of the satellite at point $a$ to that at point $b$ is

normal

Figure shows the variation of the gravitatioal acceleration $a_g$ of four planets with the radial distance $r$ from the centre ofthe planet for $r \ge $ radius of the planet. Plots $1$ and $2$ coincide for $r \ge {R_2}$ and plots $3$ and $4$ coincide for $r \ge {R_4}$ . The sequence of the planets in the descending order of their densities is

normal

The dependence of acceleration due to gravity $'g'$ on the distance $'r'$ from the centre of the earth, assumed to be a sphere of radius $R$ of uniform density is as shown in figure below

normal

A body of mass $m$ falls from a height $R$ above the surface of the earth, where $R$ is the radius of the earth. What is the velocity attained by the body on reaching the ground? (Acceleration due to gravity on the surface of the earth is $g$ )

normal