The gravitational potential at a point above | vedclass

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

Question

(A) Let $R_E$ be the radius of the Earth and $h$ be the height of the point above the surface. The distance from the center of the Earth is $r = R_E +

Vedclass · Accepted Answer

$1600$

Vedclass · Answer

(A) Let $R_E$ be the radius of the Earth and $h$ be the height of the point above the surface. The distance from the center of the Earth is $r = R_E + h$.Gravitational potential $V = -\frac{G M_E}{r} = -5.12 	imes 10^7 \,J/kg$ ... $(i)$Acceleration due to gravity $g' = \frac{G M_E}{r^2} = 6.4 \,m/s^2$ ... $(ii)$Dividing equation $(i)$ by equation $(ii)$:$\frac{V}{g'} = \frac{-G M_E / r}{G M_E / r^2} = -r$$r = -\frac{V}{g'} = -\frac{-5.12 	imes 10^7}{6.4} = 0.8 	imes 10^7 \,m = 8000 \,km$Since $r = R_E + h$, we have $h = r - R_E = 8000 \,km - 6400 \,km = 1600 \,km$.

The gravitational potential at a point above the surface of the Earth is $-5.12 \times 10^7 \,J/kg$ and the acceleration due to gravity at that point is $6.4 \,m/s^2$. Assume that the mean radius of the Earth is $6400 \,km$. The height of this point above the Earth's surface is: (in $\,km$)

Similar Questions

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 $R_{e} = 6400 \ km$)

Starting from the centre of the earth having radius $R$,the variation of $g$ (acceleration due to gravity) is shown by:

An astronaut inside a small spaceship orbiting around the earth cannot detect gravity. If the space station orbiting around the earth has a large size,can he hope to detect gravity?

Acceleration due to gravity at a height $h$ is equal to that at a depth $d$ below the surface of the earth,if

$A$ body weighs $500 \,N$ on the surface of the earth. At what distance below the surface of the earth will it weigh $250 \,N$ (in $\,km$)? (Radius of earth, $R = 6400 \,km$)

Vedclass Test Series

Exam Paper Generator

Online Exam Module