JEE Main · 2022 · 25 Jul 2022 · Shift 2 · Gravitation

An object is taken to a height above the surface of earth at a distance

\frac{5}{4} R

from the centre of the earth. Where radius of earth,

R = 6400 km

. The percentage decrease in the weight of the object will be

(A) $36%$ ✓ Correct
(B) $50%$
(C) $64%$
(D) $25%$

Answer: (A)

Solution

At distance

r = \frac{5 R}{4}

from Earth's center, the height above the surface is

h = \frac{5 R}{4} - R = \frac{R}{4}

.

The effective gravity at this height:

g_{eff} = \frac{g}{( 1 + \frac{h}{R} ) ^{2}} = \frac{g}{( 1 + \frac{1}{4} ) ^{2}} = \frac{g}{( 5/4 ) ^{2}} = \frac{16 g}{25}

Percentage change in weight:

\frac{g _{eff} - g}{g} \times 100 = \frac{\frac{16 g}{25} - g}{g} \times 100 = \frac{- 9 g}{25 g} \times 100 = - 36%

The weight decreases by 36%.

JEE Main · 2022 · 25 Jul 2022 · Shift 2 · 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 →