If the acceleration due to gravity experience | vedclass

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

Question

(C) The acceleration due to gravity at a height $h$ above the Earth's surface is given by $g_h = g(1 - \frac{2h}{R_e})$ for $h \ll R_e$.The accelerati

Vedclass · Accepted Answer

$2$

Vedclass · Answer

(C) The acceleration due to gravity at a height $h$ above the Earth's surface is given by $g_h = g(1 - \frac{2h}{R_e})$ for $h \ll R_e$.The acceleration due to gravity at a depth $d$ below the Earth's surface is given by $g_d = g(1 - \frac{d}{R_e})$.According to the problem,$g_h = g_d$,so:$g(1 - \frac{2h}{R_e}) = g(1 - \frac{d}{R_e})$Canceling $g$ from both sides and simplifying:$1 - \frac{2h}{R_e} = 1 - \frac{d}{R_e}$$\frac{2h}{R_e} = \frac{d}{R_e}$$d = 2h$Given that $d = \alpha h$,we compare the two expressions:$\alpha h = 2h$$\alpha = 2$.

If the acceleration due to gravity experienced by a point mass at a height $h$ above the surface of the Earth is the same as the acceleration due to gravity at a depth $d = \alpha h$ $(h \ll R_{e})$ from the Earth's surface,then the value of $\alpha$ will be: (use $R_{e} = 6400 \ km$)

Similar Questions

If the mass of the Sun were ten times smaller and the universal gravitational constant were ten times larger in magnitude,which of the following is not correct?

If the radius of the earth contracts by $2\%$ and its mass remains the same,then the weight of a body at the earth's surface:

The mass and diameter of a planet have twice the value of the corresponding parameters of Earth. Acceleration due to gravity on the surface of the planet is ........ $m/s^2$.

$R$ and $r$ are the radii of the Earth and Moon respectively. $\rho_e$ and $\rho_m$ are the densities of the Earth and Moon respectively. The ratio of the accelerations due to gravity on the surfaces of the Earth and Moon is

If acceleration due to gravity at distance $d < R$ from the centre of the Earth is $\beta$,then its value at distance $d$ above the surface of the Earth will be [where $R$ is the radius of the Earth].

Vedclass Test Series

Exam Paper Generator

Online Exam Module