At a height of h km from the surface of the E | vedclass

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

Question

(D) The gravitational potential at a height $h$ from the surface of the Earth is given by $V_h = -\frac{GM}{R+h} = -5.4 	imes 10^7\, J kg^{-1}$.The a

Vedclass · Accepted Answer

$2600$

Vedclass · Answer

(D) The gravitational potential at a height $h$ from the surface of the Earth is given by $V_h = -\frac{GM}{R+h} = -5.4 	imes 10^7\, J kg^{-1}$.The acceleration due to gravity at the same height is $g_h = \frac{GM}{(R+h)^2} = 6.0\, m s^{-2}$.We can relate these two expressions as $g_h = \frac{GM}{(R+h)^2} = \frac{1}{R+h} \left( \frac{GM}{R+h} ight) = \frac{-V_h}{R+h}$.Rearranging for $(R+h)$,we get $R+h = \frac{-V_h}{g_h}$.Substituting the given values: $R+h = \frac{-(-5.4 	imes 10^7)}{6.0} = \frac{5.4 	imes 10^7}{6.0} = 0.9 	imes 10^7 = 9.0 	imes 10^6\, m$.Converting the radius of the Earth to meters: $R = 6400\, km = 6.4 	imes 10^6\, m$.Now,$h = (R+h) - R = 9.0 	imes 10^6 - 6.4 	imes 10^6 = 2.6 	imes 10^6\, m$.Converting back to kilometers: $h = 2600\, km$.

At a height of $h$ $km$ from the surface of the Earth,the gravitational potential and the value of $g$ are $-5.4 \times 10^7\, J kg^{-1}$ and $6.0\, m s^{-2}$ respectively. Take the radius of the Earth as $6400\, km$.

Similar Questions

The acceleration due to gravity is $g$ at a point distant $r$ from the centre of the Earth of radius $R$. If $r < R$,then:

If the Earth suddenly stops rotating,then the weight of an object of mass $m$ at the equator will $[\omega$ is the angular speed of the Earth and $R$ is its radius]

The weight of a body of mass $m$ decreases by $1\%$ when it is taken to a height $h$ above the surface of the Earth. What is the percentage decrease in its weight when it is taken to a depth $h$ below the surface of the Earth?

$A$ planet has double the mass of the earth. Its average density is equal to that of the earth. An object weighing $W$ on earth will weigh on that planet:

The acceleration due to gravity at height $h$ above the earth if $h \ll R$ (radius of earth) is given by

Vedclass Test Series

Exam Paper Generator

Online Exam Module