Approximate height from surface of earth at which weight of body becomes frac{1}{3} of its weight on

English

Gujarati

Hindi

7.Gravitation

medium

The approximate height from the surface of earth at which the weight of the body becomes $\frac{1}{3}$ of its weight on the surface of earth is $..........km$ : [Radius of earth $R =6400 \,km$ and $\sqrt{3}=1.732]$

A

$3840$

B

$4685$

C

$2133$

D

$4267$

(JEE MAIN-2022)

Solution

$Mg ^{\prime}=\frac{ M }{3}\, g$

$g ^{\prime}=\frac{ g }{3}$

$g^{\prime}=g\left(\frac{R}{R+h}\right)^{2}=\frac{g}{3}$

$\frac{R}{R+h}=\frac{1}{\sqrt{3}}$

$h =(\sqrt{3}-1) \,R$

$=(1.732-1) 6400$

$h =4685 \,km$

Standard 11

Physics

Share

Similar Questions

Two planets $A$ and $B$ have same mass and radii $(R)$ . The variation of density of the planets with distance from centre is shown in the following diagrams. The ratio of acceleration due to gravity at the surface of the planets $A$ and $B$ will be

medium

The variation of acceleration due to gravity $g$ with distance $d$ from centre of the earth is best represented by ($R =$ Earth's radius)

medium

(JEE MAIN-2022)

The weight of an astronaut, in an artificial satellite revolving around the earth, is

easy

A newly discovered planet has a density eight times the density of the earth and a radius twice the radius of the earth. The time taken by $2\, kg$ mass to fall freely through a distance $S$ near the surface of the earth is $1$ second. Then the time taken for a $4\, kg$ mass to fall freely through the same distance $S$ near the surface of the new planet is ……. $\sec$.

normal

The value of acceleration due to gravity at Earth’s surface is $9.8\, m\,s^{-2}$. The altitude above its surface at which the acceleration due to gravity decreases to $4.9\, m\,s^{-2}$, is close to: (Radius of earth $= 6.4\times10^6\, m$)

medium

(JEE MAIN-2019)