Intensity of Gravitational Field | JEE Main previous year questions with Solutions

Q 1 :

A 90 kg body placed at 2R distance from surface of earth experiences gravitational pull of (R = Radius of earth, $g = 10 m s^{- 2}$ ) [2024]

100 N
300 N
120 N
225 N

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(1)

Acceleration due to gravity at height $h$ from earth's surface

$g_{h} = \frac{G M}{{(R + h)}^{2}}$

$g_{h} = \frac{G M}{9 R^{2}} = \frac{g_{s}}{9} (∵ h = 2 R)$

Here $g_{s} =$ gravitational acceleration at surface

Gravitational Pull $m g_{s} = 90 \times \frac{g_{s}}{9} = 100 N$

Q 2 :

Assuming the earth to be a sphere of uniform mass density, a body weighed 300 N on the surface of earth. How much it would weigh at R/4 depth under surface of earth? [2024]

300 N
75 N
225 N
375 N

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(3)

At surface: $m g_{s} = 300 N \Rightarrow m = \frac{300}{g_{s}}$

Gravitational field at $\frac{R}{4}$ depth under surface, $g_{d} = g_{s} [1 - \frac{d}{R}]$

$g_{d} = g_{s} [1 - \frac{R}{4 R}] = \frac{3 g_{s}}{4}$

Weight at depth, $W_{d} = m \times g_{d} = m \times \frac{3 g_{s}}{4} = \frac{3}{4} \times 300 = 225 N$

Q 3 :

The acceleration due to gravity on the surface of earth is g. If the diameter of earth reduces to half of its original value and mass remains constant, then acceleration due to gravity on the surface of earth would be [2024]

g/4
2g
g/2
4g

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(4)

$g = \frac{G M}{R^{2}} \Rightarrow g \propto \frac{1}{R^{2}}$

$g_{2} = 4 g_{1} (R_{2} = \frac{R_{1}}{2})$

Q 4 :

If R is the radius of the earth and the acceleration due to gravity on the surface of earth is $g = π^{2} m / s^{2}$ , then the length of the second's pendulum at a height $h = 2 R$ from the surface of earth will be [2024]

$\frac{2}{9} m$
$\frac{1}{9} m$
$\frac{4}{9} m$
$\frac{8}{9} m$

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(2)

$g = \frac{G M}{R^{2}} = π^{2}$

$g' = \frac{G M}{9 R^{2}} = \frac{g}{9} = \frac{π^{2}}{9}$

We know, $T = 2 π \sqrt{\frac{l}{g}}$

Since the time period of second pendulum is 2 sec.

$2 = 2 π \sqrt{\frac{l \times 9}{π^{2}}}$

On solving, $l = \frac{1}{9} m$

Q 5 :

At what distance above and below the surface of the earth a body will have same weight? (take radius of earth as R). [2024]

$\sqrt{5} R - R$
$\frac{\sqrt{3} R - R}{2}$
$\frac{R}{2}$
$\frac{\sqrt{5} R - R}{2}$

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(4)

Below the surface of the earth, $W_{d e p t h} = \frac{G M m (R - h)}{R^{3}}$

Above the surface of the earth, $W_{a b o v e} = \frac{G M m}{{(R + h)}^{2}}$

If the body will have same weight, $g_{p} = g_{q}$

$\frac{G M m (R - h)}{R^{3}} = \frac{G M m}{{(R + h)}^{2}}$

$R^{3} = {(R + h)}^{2} (R - h) \Rightarrow h^{2} + R h - R^{2} = 0$

$\Rightarrow h = \frac{R}{2} (\sqrt{5} - 1)$

Q 6 :

A simple pendulum is placed at a place where its distance from the earth's surface is equal to the radius of the earth. If the length of the string is 4m, then the time period of small oscillations will be ___________ s. $[t a k e g = π^{2}$ $m s^{- 2}]$ [2024]

(8) $T = 2 π \sqrt{\frac{l}{g_{eff}}}$

$g = \frac{G M}{R^{2}}, at a height, h, g = \frac{G M}{{(R + h)}^{2}}$

$g_{eff} = g {(\frac{R}{R + h})}^{2}, g_{eff} = g {(\frac{R}{2 R})}^{2}$

$g_{eff} = \frac{g}{4}$

$∴ T = 2 π \sqrt{\frac{l}{g_{eff}}} = 2 π \sqrt{\frac{4 \times 4}{g}} = \frac{(2 π) (4)}{\sqrt{g}}$

$Given, g = π^{2}$

$T = 8 \sec$

Q 7 :

A metal wire of uniform mass density having length L and mass M is bent to form a semicircular arc, and a particle of mass m is placed at the centre of the arc. The gravitational force on the particle by the wire is _____. [2024]

0
$\frac{G M m π}{2 L^{2}}$
$\frac{2 G M m π}{L^{2}}$
$\frac{G M m π}{L^{2}}$

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(3)

$E_{g} = \frac{2 \cdot G \cdot λ}{R} = \frac{2 G M}{L \cdot R}$

$also, π R = L \Rightarrow R = \frac{L}{π}$

$∴ E_{g} = \frac{2 G M}{L \cdot \frac{L}{π}} = \frac{2 G M π}{L^{2}}$

$F = m E_{g} = \frac{2 G M m π}{L^{2}}$

Q 8 :

Acceleration due to gravity on the surface of earth is 'g'. If the diameter of earth is reduced to one third of its original value and mass remains unchanged, then the acceleration due to gravity on the surface of the earth is ________ g. [2025]

(9)

$∵$ Acceleration due to gravity on surface, $g = \frac{G M}{R_{e}^{2}}$

Now since diameter is reduced to $1 / 3^{rd}$ , radius also reduces to $1 / 3^{rd}$ , keeping mass constant.

New value of acceleration due to gravity on Earth's surface,

$g' = \frac{G M}{{(\frac{R_{e}}{3})}^{2}} = 9 \frac{G M}{R_{e}^{2}} = 9 g$

Q 9 :

The weight of a body at the surface of earth is 18 N. The weight of the body at an altitude of 3200 km above the earth’s surface is (given, radius of earth $R_{e} = 6400$ km) [2023]

19.6 N
9.8 N
4.9 N
8 N

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(4)

$Acceleration due to gravity at height h$

$g' = \frac{g}{{[1 + \frac{h}{R}]}^{2}}$

$So weight at given height$

$m g' = \frac{m g}{{[1 + \frac{h}{R}]}^{2}} = \frac{18}{{[1 + \frac{1}{2}]}^{2}} = 8 N$

Q 10 :

Given below are two statements: [2023]

Statement I: Acceleration due to earth’s gravity decreases as you go ‘up’ or ‘down’ from earth’s surface.

Statement II: Acceleration due to earth’s gravity is same at a height ‘ $h$ ’ and depth ‘ $d$ ’ from earth’s surface, if $h = d .$

In the light of above statements, choose the most appropriate answer from the options given below:

Statement I is correct but statement II is incorrect
Both Statement I and Statement II are incorrect
Both Statement I and II are correct
Statement I is incorrect but statement II is correct

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(1)

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

$g' = g {1 - \frac{d}{R}}$

Statement I is correct & Statement II is incorrect.

Q 11 :

At a certain depth “ $d$ ” below surface of earth, value of acceleration due to gravity becomes four times that of its value at a height 3R above earth surface, where R is radius of earth (Take R = 6400 km). The depth $d$ is equal to [2023]

5260 km
640 km
2560 km
4800 km

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(4)

$\frac{G M}{R^{2}} [1 - \frac{d}{R}] = \frac{4 \times G M}{{(4 R)}^{2}}$

$1 - \frac{d}{R} = \frac{1}{4} \Rightarrow \frac{d}{R} = \frac{3}{4} \Rightarrow d = \frac{3}{4} R$

$d = 4800 km$

Q 12 :

A body of weight $W$ is projected vertically upwards from the earth's surface to reach a height above the earth which is equal to nine times the radius of the earth. The weight of the body at that height will be [2023]

$\frac{W}{91}$
$\frac{W}{100}$
$\frac{W}{9}$
$\frac{W}{3}$

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(2)

$g' = \frac{G M}{{(10 R)}^{2}} = (\frac{g}{100})$

$W' = (\frac{W}{100})$

Q 13 :

Given below are two statements: [2023]

Statement I: Acceleration due to gravity is different at different places on the surface of earth.

Statement II: Acceleration due to gravity increases as we go down below the earth’s surface.

In the light of the above statements, choose the correct answer from the options given below:

Both Statement I and Statement II are true
Both Statement I and Statement II are false
Statement I is true but Statement II is false
Statement I is false but Statement II is true

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(3)

$g_{eff} = g - ω^{2} R_{e} \sin^{2} θ$

$g_{eff} = g (1 - \frac{d}{R_{e}})$

Q 14 :

The weight of a body on the surface of the earth is 100 N. The gravitational force on it when taken at a height from the surface of earth, equal to one-fourth the radius of the earth, is: [2023]

100 N
64 N
50 N
25 N

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(2)

$\Rightarrow g' = \frac{g R^{2}}{r^{2}} = \frac{g R^{2}}{{(R + \frac{R}{4})}^{2}} = \frac{16 g}{25}$

$∴$ $Weight = \frac{16}{25} \times 100 = 64 N$

Q 15 :

The weight of a body on the earth is 400 N. Then the weight of the body when taken to a depth half of the radius of the earth will be: [2023]

300 N
100 N
Zero
200 N

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(4)

$W = m g = 400 N$

$At depth d, gravity g' = g (1 - \frac{d}{R})$

$For d = \frac{R}{2}, g' = g (1 - \frac{d}{2 R}) = \frac{g}{2}$

$W' = m g' = \frac{m g}{2} = 200 N$

Q 16 :

The acceleration due to gravity at height $h$ above the earth, if $h ≪ R$ (radius of earth), is given by [2023]

$g' = g (1 - \frac{2 h}{R})$
$g' = g (1 - \frac{h}{2 R})$
$g' = g (1 - \frac{2 h^{2}}{R^{2}})$
$g' = g (1 - \frac{h^{2}}{2 R^{2}})$

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(1)

$For a point outside the surface of Earth, g = \frac{G M}{r^{2}}$

$r = distance from centre of Earth$

$\Rightarrow g (h) = \frac{G M}{{(R + h)}^{2}} = \frac{G M}{R^{2} {(1 + \frac{h}{R})}^{2}}$

$\Rightarrow g (h) = \frac{G M}{R^{2}} {(1 + \frac{h}{R})}^{- 2}$

$If h ≪ R, {(1 + \frac{h}{R})}^{- 2} \approx 1 - \frac{2 h}{R}$

$\Rightarrow g (h) = \frac{G M}{R^{2}} (1 - \frac{2 h}{R})$

$\Rightarrow g (h) = g_{surface} (1 - \frac{2 h}{R}), \frac{G M}{R^{2}} = g_{surface}$

Q 17 :

Assuming the earth to be a sphere of uniform mass density, the weight of a body at a depth $d = \frac{R}{2}$ from the surface of the earth, if its weight on the surface of the earth is 200 N, will be (Given R = radius of earth) [2023]

400 N
500 N
300 N
100 N

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(4)

$M = \frac{W}{g} = \frac{200}{10} = 20 kg$

$Acceleration due to gravity at a depth$

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

$d = depth from surface, d = \frac{R}{2}$

$g' = g (1 - \frac{R / 2}{R}) = \frac{g}{2} = {5 m/s}^{2}$

$Weight = m \times g' = 20 \times 5 = 100 N$

Q 18 :

Given below are two statements: [2023]

Statement I: Rotation of the earth shows effect on the value of acceleration due to gravity (g).

Statement II: The effect of rotation of the earth on the value of 'g' at the equator is minimum and that at the pole is maximum.

In the light of the above statements, choose the correct answer from the options given below:

Statement I is false but Statement II is true.
Statement I is true but Statement II is false.
Both Statement I and Statement II are true.
Both Statement I and Statement II are false.

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(2)

$Statement I is true due to centrifugal force.$

$Statement II is incorrect.$

$At pole: g = g_{s} (no effect)$

$At equator: g = g_{s} - r ω^{2} \cos^{2} λ = g_{s} - r ω^{2}$

$∴$ $\cos^{2} λ is maximum at λ = 0 ° (i.e., at equator)$

$Effect is maximum at equator.$

Q 19 :

Two planets A and B of radii R and 1.5 R have densities $ρ$ and $ρ / 2$ respectively. The ratio of acceleration due to gravity at the surface of B to A is [2023]

2 : 3
2 : 1
3 : 4
4 : 3

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(3)

$g = \frac{G M}{R^{2}} = \frac{4}{3} π G ρ R$

$∴$ $\frac{g_{2}}{g_{1}} = \frac{ρ_{2}}{ρ_{1}} \times \frac{R_{2}}{R_{1}} = \frac{1}{2} \times 1.5 = \frac{3}{4}$

Topic Question Set

Q 1 :

A 90 kg body placed at 2R distance from surface of earth experiences gravitational pull of (R = Radius of earth, $g = 10 m s^{- 2}$ ) [2024]

Q 2 :

Assuming the earth to be a sphere of uniform mass density, a body weighed 300 N on the surface of earth. How much it would weigh at R/4 depth under surface of earth? [2024]

Q 3 :

The acceleration due to gravity on the surface of earth is g. If the diameter of earth reduces to half of its original value and mass remains constant, then acceleration due to gravity on the surface of earth would be [2024]

Q 4 :

If R is the radius of the earth and the acceleration due to gravity on the surface of earth is $g = π^{2} m / s^{2}$ , then the length of the second's pendulum at a height $h = 2 R$ from the surface of earth will be [2024]

Q 5 :

At what distance above and below the surface of the earth a body will have same weight? (take radius of earth as R). [2024]

Q 6 :

A simple pendulum is placed at a place where its distance from the earth's surface is equal to the radius of the earth. If the length of the string is 4m, then the time period of small oscillations will be ___________ s. $[t a k e g = π^{2}$ $m s^{- 2}]$ [2024]

Q 7 :

A metal wire of uniform mass density having length L and mass M is bent to form a semicircular arc, and a particle of mass m is placed at the centre of the arc. The gravitational force on the particle by the wire is _____. [2024]

Q 8 :

Acceleration due to gravity on the surface of earth is 'g'. If the diameter of earth is reduced to one third of its original value and mass remains unchanged, then the acceleration due to gravity on the surface of the earth is ________ g. [2025]

Q 9 :

The weight of a body at the surface of earth is 18 N. The weight of the body at an altitude of 3200 km above the earth’s surface is (given, radius of earth $R_{e} = 6400$ km) [2023]

Q 11 :

At a certain depth “ $d$ ” below surface of earth, value of acceleration due to gravity becomes four times that of its value at a height 3R above earth surface, where R is radius of earth (Take R = 6400 km). The depth $d$ is equal to [2023]

Q 12 :

A body of weight $W$ is projected vertically upwards from the earth's surface to reach a height above the earth which is equal to nine times the radius of the earth. The weight of the body at that height will be [2023]

Q 14 :

The weight of a body on the surface of the earth is 100 N. The gravitational force on it when taken at a height from the surface of earth, equal to one-fourth the radius of the earth, is: [2023]

Q 15 :

The weight of a body on the earth is 400 N. Then the weight of the body when taken to a depth half of the radius of the earth will be: [2023]

Q 16 :

The acceleration due to gravity at height $h$ above the earth, if $h ≪ R$ (radius of earth), is given by [2023]

Q 17 :

Assuming the earth to be a sphere of uniform mass density, the weight of a body at a depth $d = \frac{R}{2}$ from the surface of the earth, if its weight on the surface of the earth is 200 N, will be (Given R = radius of earth) [2023]

Q 19 :

Two planets A and B of radii R and 1.5 R have densities $ρ$ and $ρ / 2$ respectively. The ratio of acceleration due to gravity at the surface of B to A is [2023]

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Topic Question Set

Q 1 : A 90 kg body placed at 2R distance from surface of earth experiences gravitational pull of (R = Radius of earth, g=10ms-2) [2024]

Q 2 : Assuming the earth to be a sphere of uniform mass density, a body weighed 300 N on the surface of earth. How much it would weigh at R/4 depth under surface of earth? [2024]

Q 3 : The acceleration due to gravity on the surface of earth is g. If the diameter of earth reduces to half of its original value and mass remains constant, then acceleration due to gravity on the surface of earth would be [2024]

Q 4 : If R is the radius of the earth and the acceleration due to gravity on the surface of earth is g=π2m/s2, then the length of the second's pendulum at a height h=2R from the surface of earth will be [2024]

Q 5 : At what distance above and below the surface of the earth a body will have same weight? (take radius of earth as R). [2024]

Q 6 : A simple pendulum is placed at a place where its distance from the earth's surface is equal to the radius of the earth. If the length of the string is 4m, then the time period of small oscillations will be ___________ s. [take g=π2 ms-2] [2024]

Q 7 : A metal wire of uniform mass density having length L and mass M is bent to form a semicircular arc, and a particle of mass m is placed at the centre of the arc. The gravitational force on the particle by the wire is _____. [2024]

Q 8 : Acceleration due to gravity on the surface of earth is 'g'. If the diameter of earth is reduced to one third of its original value and mass remains unchanged, then the acceleration due to gravity on the surface of the earth is ________ g. [2025]

Q 9 : The weight of a body at the surface of earth is 18 N. The weight of the body at an altitude of 3200 km above the earth’s surface is (given, radius of earth Re=6400 km) [2023]

Q 11 : At a certain depth “d” below surface of earth, value of acceleration due to gravity becomes four times that of its value at a height 3R above earth surface, where R is radius of earth (Take R = 6400 km). The depth d is equal to [2023]

Q 12 : A body of weight W is projected vertically upwards from the earth's surface to reach a height above the earth which is equal to nine times the radius of the earth. The weight of the body at that height will be [2023]

Q 14 : The weight of a body on the surface of the earth is 100 N. The gravitational force on it when taken at a height from the surface of earth, equal to one-fourth the radius of the earth, is: [2023]

Q 15 : The weight of a body on the earth is 400 N. Then the weight of the body when taken to a depth half of the radius of the earth will be: [2023]

Q 16 : The acceleration due to gravity at height h above the earth, if h≪R (radius of earth), is given by [2023]

Q 17 : Assuming the earth to be a sphere of uniform mass density, the weight of a body at a depth d=R2 from the surface of the earth, if its weight on the surface of the earth is 200 N, will be (Given R = radius of earth) [2023]

Q 19 : Two planets A and B of radii R and 1.5 R have densities ρ and ρ/2 respectively. The ratio of acceleration due to gravity at the surface of B to A is [2023]

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Q 1 :

A 90 kg body placed at 2R distance from surface of earth experiences gravitational pull of (R = Radius of earth, $g = 10 m s^{- 2}$ ) [2024]

Q 2 :

Assuming the earth to be a sphere of uniform mass density, a body weighed 300 N on the surface of earth. How much it would weigh at R/4 depth under surface of earth? [2024]

Q 3 :

The acceleration due to gravity on the surface of earth is g. If the diameter of earth reduces to half of its original value and mass remains constant, then acceleration due to gravity on the surface of earth would be [2024]

Q 4 :

If R is the radius of the earth and the acceleration due to gravity on the surface of earth is $g = π^{2} m / s^{2}$ , then the length of the second's pendulum at a height $h = 2 R$ from the surface of earth will be [2024]

Q 5 :

At what distance above and below the surface of the earth a body will have same weight? (take radius of earth as R). [2024]

Q 6 :

A simple pendulum is placed at a place where its distance from the earth's surface is equal to the radius of the earth. If the length of the string is 4m, then the time period of small oscillations will be ___________ s. $[t a k e g = π^{2}$ $m s^{- 2}]$ [2024]

Q 7 :

A metal wire of uniform mass density having length L and mass M is bent to form a semicircular arc, and a particle of mass m is placed at the centre of the arc. The gravitational force on the particle by the wire is _____. [2024]

Q 8 :

Acceleration due to gravity on the surface of earth is 'g'. If the diameter of earth is reduced to one third of its original value and mass remains unchanged, then the acceleration due to gravity on the surface of the earth is ________ g. [2025]

Q 9 :

The weight of a body at the surface of earth is 18 N. The weight of the body at an altitude of 3200 km above the earth’s surface is (given, radius of earth $R_{e} = 6400$ km) [2023]

Q 11 :

At a certain depth “ $d$ ” below surface of earth, value of acceleration due to gravity becomes four times that of its value at a height 3R above earth surface, where R is radius of earth (Take R = 6400 km). The depth $d$ is equal to [2023]

Q 12 :

A body of weight $W$ is projected vertically upwards from the earth's surface to reach a height above the earth which is equal to nine times the radius of the earth. The weight of the body at that height will be [2023]

Q 14 :

The weight of a body on the surface of the earth is 100 N. The gravitational force on it when taken at a height from the surface of earth, equal to one-fourth the radius of the earth, is: [2023]

Q 15 :

The weight of a body on the earth is 400 N. Then the weight of the body when taken to a depth half of the radius of the earth will be: [2023]

Q 16 :

The acceleration due to gravity at height $h$ above the earth, if $h ≪ R$ (radius of earth), is given by [2023]

Q 17 :

Assuming the earth to be a sphere of uniform mass density, the weight of a body at a depth $d = \frac{R}{2}$ from the surface of the earth, if its weight on the surface of the earth is 200 N, will be (Given R = radius of earth) [2023]

Q 19 :

Two planets A and B of radii R and 1.5 R have densities $ρ$ and $ρ / 2$ respectively. The ratio of acceleration due to gravity at the surface of B to A is [2023]