Acceleration due to Gravity and its Variation

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JEE Main 2020, 5 Sep Shift-I

The value of the acceleration due to gravity is $g_{1}$ at a height $h = \frac{R}{2}$ (where, $R =$ 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

\frac{7}{9}

(B)

\frac{1}{3}

(C)

\frac{4}{9}

(D)

\frac{5}{9}

JEE Main 2017

LEVELJEE Main

The variation of acceleration due to gravity $g$ with distance $d$ from centre of the Earth is best represented by ( $R =$ Earth's radius)

JEE Main 2021, 31 Aug Shift-II

LEVELJEE Main

If $R_{E}$ be the radius of Earth, then the ratio between the acceleration due to gravity at a depth $r$ below and a height $r$ above the Earth surface is (Given, $r < R_{E}$ )

(A)

1 - \frac{r}{R _{E}} - \frac{r ^{2}}{R _{E}^{2}} - \frac{r ^{3}}{R _{E}^{3}}

(B)

1 + \frac{r}{R _{E}} + \frac{r ^{2}}{R _{E}^{2}} + \frac{r ^{3}}{R _{E}^{3}}

(C)

1 + \frac{r}{R _{E}} - \frac{r ^{2}}{R _{E}^{2}} + \frac{r ^{3}}{R _{E}^{3}}

(D)

1 + \frac{r}{R _{E}} - \frac{r ^{2}}{R _{E}^{2}} - \frac{r ^{3}}{R _{E}^{3}}

JEE Main 2020, 7 Jan Shift-II

LEVELJEE Main

A box weighs $196 N$ on a spring balance at the north pole. Its weight recorded on the same balance, if it is shifted to the equator is close to (Take, $g = 10 ms^{- 2}$ at the north pole and the radius of the earth $= 6400 km$ )

(A)

195.66 N

(B)

195.32 N

(C)

194.66 N

(D)

194.32 N

JEE Main 2019, 10 April Shift-I

LEVELJEE Main

The value of acceleration due to gravity at earth's surface is $9.8 ms^{- 2}$ . The altitude above its surface at which the acceleration due to gravity decreases to $4.9 ms^{- 2}$ , is close to (Take, radius of earth = $6.4 \times 1 0^{6} m$ )

(A)

9.0 \times 1 0^{6} m

(B)

2.6 \times 1 0^{6} m

(C)

6.4 \times 1 0^{6} m

(D)

1.6 \times 1 0^{6} m

LEVELJEE Main

If $g_{E}$ and $g_{M}$ are the accelerations due to gravity on the surfaces of the earth and the moon respectively and if Millikan's oil drop experiment could be performed on the two surfaces, one will find the ratio $\frac{electronic charge on the moon}{electronic charge on the earth}$ to be

(A)

1

(B)

zero

(C)

\frac{g _{E}}{g _{M}}

(D)

\frac{g _{M}}{g _{E}}

JEE Main 2021, 20 July Shift-I

LEVELJEE Main

A person whose mass is $100 kg$ travels from Earth to Mars in a spaceship. Neglect all other objects in sky and take acceleration due to gravity on the surface of the Earth and Mars as $10 m/s^{2}$ and $4 m/s^{2}$ , respectively. Identify from the below figures, the curve that fits best for the weight of the passenger as a function of time.

JEE Main 2021, 25 July Shift-II

LEVELJEE Main

Consider a planet in some solar system which has a mass double the mass of Earth and density equal to the average density of Earth. If the weight of an object on Earth is $w$ , the weight of the same object on that planet will be

(A)

2 w

(B)

w

(C)

2^{1/3} w

(D)

2 w

LEVELBoard

Average density of the earth

(A)

does not depend on

g

(B)

is a complex function of

g

(C)

is directly proportional to

g

(D)

is inversely proportional to

g

JEE Main 2019, 12 April Shift-II

LEVELJEE Main

The ratio of the weights of a body on the earth's surface, so that on the surface of a planet is 9 : 4. The mass of the planet is $\frac{1}{9}$ th of that of the earth. If $R$ is the radius of the earth, what is the radius of the planet? (Take, the planets to have the same mass density)

(A)

\frac{R}{3}

(B)

\frac{R}{4}

(C)

\frac{R}{9}

(D)

\frac{R}{2}

JEE Main 2021, 18 March Shift-II

LEVELJEE Main

If the angular velocity of Earth's spin is increased such that the bodies at the equator start floating, the duration of the day would be approximately (Take $g = 10 ms^{- 2}$ , the radius of Earth, $R = 6400 \times 1 0^{3} m$ , take $π = 3.14$ )

JEE Main 2021, 26 Feb Shift-II

LEVELJEE Main

In the reported figure of Earth, the value of acceleration due to gravity is same at point $A$ and $C$ but it is smaller than that of its value at point $B$ (surface of the Earth). The value of $O A : A B$ will be $x : y$ . The value of $x$ is .......... .

JEE Main 2020, 2 Sep Shift-II

LEVELJEE Main

The height $h$ at which the weight of a body will be the same as that at the same depth $h$ from the surface of the earth is (Radius of the earth is $R$ and effect of the rotation of the earth is neglected)

(A)

\frac{5}{2} R - R

(B)

\frac{R}{2}

(C)

\frac{5 R - R}{2}

(D)

\frac{3 R - R}{2}

LEVELJEE Main

The height at which the acceleration due to gravity becomes $\frac{g}{9}$ (where, $g$ is the acceleration due to gravity on the surface of the earth) in terms of $R$ , the radius of the earth is

(A)

2 R

(B)

\frac{R}{3}

(C)

\frac{R}{2}

(D)

2 R

LEVELJEE Main

The change in the value of $g$ at a height $h$ above the surface of the earth is the same as at a depth $d$ below the surface of earth. When both $d$ and $h$ are much smaller than the radius of earth, then which one of the following is correct?

(A)

d = \frac{h}{2}

(B)

d = \frac{3 h}{2}

(C)

d = 2 h

(D)

d = h

JEE Main 2020, 5 Sep Shift-II

LEVELJEE Main

The acceleration due to gravity on the earth's surface at the poles is $g$ and angular velocity of the earth about the axis passing through the pole is $ω$ . An object is weighed at the equator and at a height $h$ above the poles by using a spring balance. If the weights are found to be same, then $h$ is ( $h ≪ R$ , where $R$ is the radius of the earth)

(A)

\frac{R ^{2} ω ^{2}}{2 g}

(B)

\frac{R ^{2} ω ^{2}}{g}

(C)

\frac{R ^{2} ω ^{2}}{4 g}

(D)

\frac{R ^{2} ω ^{2}}{8 g}

JEE Main 2021, 24 Feb Shift-II

LEVELJEE Main

A body weights $49 N$ on a spring balance at the North pole. What will be its weight recorded on the same weighing machine, if it is shifted to the equator ? (Use, $g = \frac{GM}{R ^{2}} = 9.8 ms^{- 2}$ and radius of earth, $R = 6400 km$ )

(A)

49 N

(B)

48.83 N

(C)

49.83 N

(D)

49.17 N

JEE Advanced 2014

LEVELJEE Advanced

A planet of radius $R = \frac{1}{10} \times (radius of earth)$ has the same mass density as earth. Scientists dig a well of depth $\frac{R}{5}$ on it and lower a wire of the same length and of linear mass density $1 0^{- 3} kg m^{- 1}$ into it. If the wire is not touching anywhere, the force applied at the top of the wire by a person holding it in place is (take the radius of earth $= 6 \times 1 0^{6} m$ and the acceleration due to gravity of earth is $10 ms^{- 2}$ )

(A)

96 N

(B)

108 N

(C)

120 N

(D)

150 N

JEE Advanced 2001

LEVELJEE Main

A simple pendulum has a time period $T_{1}$ when on the earth's surface and $T_{2}$ when taken to a height $R$ above the earth's surface, where $R$ is the radius of the earth. The value of $\frac{T _{2}}{T _{1}}$ is

(A)

1

(B)

2

(C)

4

(D)

2

LEVELJEE Main

If the radius of the earth were to shrink by one per cent, its mass remaining the same, the acceleration due to gravity on the earth's surface would

The numerical value of the angular velocity of rotation of the earth should be \_\_\_\_\_\_\_\_ $rad/s$ in order to make the effective acceleration due to gravity at equator equal to zero. (Take $g = 9.8 m/s^{2}$ and radius of earth $R = 6400 km$ )

JEE Advanced 2023

LEVELJEE Main

Two satellites P and Q are moving in different circular orbits around the Earth (radius R). The heights of P and Q from the Earth surface are $h_{P}$ and $h_{Q}$ , respectively, where $h_{P} = R /3$ . The accelerations of P and Q due to Earth's gravity are $g_{P}$ and $g_{Q}$ , respectively. If $g_{P} / g_{Q} = 36/25$ , what is the value of $h_{Q}$ ?

(A)

\frac{3 R}{5}

(B)

\frac{R}{6}

(C)

\frac{6 R}{5}

(D)

\frac{5 R}{6}

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } The variation of acceleration due to gravity g with distance d from centre of the Earth is best represented by (R= Earth's radius)

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } If RE​ be the radius of Earth, then the ratio between the acceleration due to gravity at a depth r below and a height r above the Earth surface is (Given, r<RE​)

Average density of the earth

If the radius of the earth were to shrink by one per cent, its mass remaining the same, the acceleration due to gravity on the earth's surface would

The variation of acceleration due to gravity $g$ with distance $d$ from centre of the Earth is best represented by ( $R =$ Earth's radius)

If $R_{E}$ be the radius of Earth, then the ratio between the acceleration due to gravity at a depth $r$ below and a height $r$ above the Earth surface is (Given, $r < R_{E}$ )