JEE Main · 2020 · 05 Sep 2020 · Shift 1 · Gravitation

The value of the acceleration due to gravity is

g_{1}

at a height

h = \frac{R}{2}

(

R =

radius of the earth) from the surface of the earth. It is again equal to

g_{1}

at a depth d below the surface of the earth. The ratio

(\frac{d}{R})

equals:

(A) $\frac{7}{9}$
(B) $\frac{1}{3}$
(C) $\frac{5}{9}$ ✓ Correct
(D) $\frac{4}{9}$

Answer: (C)

Solution

Above the surface the field falls off as

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

; at

h = \frac{R}{2}

this is

g (\frac{2}{3})^{2} = \frac{4 g}{9}

. Below the surface it decreases linearly,

g_{1} = g (1 - \frac{d}{R})

. Setting the two equal,

1 - \frac{d}{R} = \frac{4}{9}

, so

\frac{d}{R} = \frac{5}{9}

JEE Main · 2020 · 05 Sep 2020 · Shift 1 · 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 →