The ratio of the height h above the surface o | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(B) The gravitational acceleration at a height $h$ above the Earth's surface is given by $g_h = g(1 - \frac{2h}{R})$,where $R$ is the radius of the Ea

Vedclass · Accepted Answer

$0.5$

Vedclass · Answer

(B) The gravitational acceleration at a height $h$ above the Earth's surface is given by $g_h = g(1 - \frac{2h}{R})$,where $R$ is the radius of the Earth.The gravitational acceleration at a depth $d$ below the Earth's surface is given by $g_d = g(1 - \frac{d}{R})$.Given that the gravitational accelerations are the same,we equate the two expressions:$g(1 - \frac{2h}{R}) = g(1 - \frac{d}{R})$Canceling $g$ from both sides:$1 - \frac{2h}{R} = 1 - \frac{d}{R}$Subtracting $1$ from both sides:$-\frac{2h}{R} = -\frac{d}{R}$Multiplying by $-R$:$2h = d$Therefore,the ratio of height to depth is:$\frac{h}{d} = \frac{1}{2} = 0.5$

The ratio of the height $h$ above the surface of the Earth to the depth $d$ below the surface of the Earth,for which the gravitational accelerations are the same (assuming small heights),is:

Similar Questions

$A$ body thrown on Earth reaches a height of $90\,m$. If the same body is thrown on a planet with $\frac{1}{10}$ of the mass and $\frac{1}{3}$ of the radius of Earth,it will reach a height of ....... $m$.

Two planets of radii in the ratio $2 : 3$ are made from the material of density in the ratio $3 : 2$. Then the ratio of acceleration due to gravity $g_1/g_2$ at the surface of the two planets will be

Acceleration due to gravity on the moon is $\frac{1}{6}$ of the acceleration due to gravity on the earth. If the ratio of densities of earth $(\rho_e)$ and moon $(\rho_m)$ is $\frac{\rho_e}{\rho_m} = \frac{5}{3}$,then the radius of the moon $R_m$ in terms of $R_e$ will be:

At a height $R$ above the earth's surface,the gravitational acceleration is ($R$ = radius of earth,$g$ = acceleration due to gravity on earth's surface).

As we move from the poles of the Earth towards the equator,what happens to the value of the acceleration due to gravity $(g)$?

Vedclass Test Series

Exam Paper Generator

Online Exam Module