JEE Main · 2009 · 12 Apr 2009 · Offline · Gravitation

The height at which the acceleration due to gravity becomes

\frac{g}{9}

(where

g =

the acceleration due to gravity on the surface of the earth) in terms of

R

, the radius of the earth is

(A)2 R✓ Correct
(B) $\frac{R}{2}$
(C) $\frac{R}{2}$
(D) $2 R$

Answer: (A)

Solution

Above the surface gravity falls off as

g^{'} = g (\frac{R}{R + h})^{2}

. Setting

g^{'} = \frac{g}{9}

gives

(\frac{R}{R + h})^{2} = \frac{1}{9}

, so

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

and hence

R + h = 3 R

, which means the height is

2 R

JEE Main · 2009 · 12 Apr 2009 · Offline · Single correct option

Practise more: all JEE Main PYQs on Gravitation →

More JEE Main questions on Gravitation

The escape velocity from a spherical planet A is 10 km/s. The escape velocity from another planet B whose density and radius are 10% of those of planet A, is ______ m/s.
JEE Main 2026View solution →
Net gravitational force at the centre of a square is found to be $F_{1}$ when four particles having mass $M, 2 M, 3 M$ and $4 M$ are placed at the four corners of the square as shown in figure and it is $F_{2}$ when the positions of $3 M$ and $4 M$ are interchanged. The ratio …
JEE Main 2026View solution →
Given below are two statements:
Statement I: A satellite is moving around earth in the orbit very close to the earth surface. The time period of revolution of satellite depends upon the density of earth.
Statement II: The time period of revolution of the satellite is …
JEE Main 2026View solution →
Three masses 200 kg, 300 kg and 400 kg are placed at the vertices of an equilateral triangle with sides 20 m. They are rearranged on the vertices of a bigger triangle of side 25 m and with the same centre. The work done in this process ______ J.
(Gravitational constant …
JEE Main 2026View solution →
Initially a satellite of 100 kg is in a circular orbit of radius $1.5 R_{E}$ . This satellite can be moved to a circular orbit of radius $3 R_{E}$ by supplying $α \times 1 0^{6} J$ of energy. The value of $α$ is ______.
(Take …
JEE Main 2026View solution →
If a body of mass 1 kg falls on the earth from infinity, it attains velocity (v) and kinetic energy (k) on reaching the surface of earth. The values of v and k respectively are ____.
(Take radius of earth to be 6400 km and $g = 9.8 m / s^{2}$ )
JEE Main 2026View solution →