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Previous Year Gravitation Question For NDA

Previous Year Gravitation Question For NDA

Previous Year Topic Name Question For NDA
Q 2734601552

Which one of the following statements is true for the relation `F=(Gm_1m_2)/(r^2)` ? (All symbols have their usual meanings)
NDA Paper 2 2017
(A)

The quantity G depends on the local value of g, acceleration due to gravity

(B)

The quantity G is greatest at the surface of the Earth

(C)

The quantity G is used only when · earth is one of the two masses

(D)

The quantity G is a universal constant

Solution:

Correct Answer is `=>` (D) The quantity G is a universal constant
Q 2304456358

A man weighing 70 kg is coming down in lift. If the cable of the lift breaks sudden the weight of the man would become
NDA Paper 2 2016
(A)

70 kg

(B)

35 kg

(C)

140 kg

(D)

Zero

Solution:

Consider the mass of the
man in the lift is m when cable breaks
as shown in the diagram.
Now, the man in the lift is in free fall.
Therefore, his acceleration is
same as acceleration due to gravity

'g'. Due to this acceleration pseudo force as the man i.s
mg upward. Therefore, weight of the man,
w=mg-mg=0
Correct Answer is `=>` (D) Zero
Q 2109523418

Suppose the force of gravitation between two bodies of equal masses is `F`. If each mass is doubled keeping the distance of separation between them unchanged, the force would become.
NDA Paper 2 2016
(A)

`F`

(B)

`2F`

(C)

`4F`

(D)

`1/4 F`

Solution:

Let mass of each body is m and separation between

the bodies isr. Gravitational force between the bodies

`F = (Gm^(2))/r^(2)`

After doubling the mass, gravitational force becomes

` F' = (G(2m)^(2))/r^(2) = (4Gm^(2))/r^(2) = 4F`
Correct Answer is `=>` (C) `4F`
Q 2159534414

Mass of a particular amount of substance

1. is the amount of matter present in it
2. does not vary from place to place
3. changes with change in gravitational force

Select the correct answer using the codes given below
NDA Paper 2 2016
(A)

`1, 2` and `3`

(B)

`1` and `2`

(C)

`2` and `3`

(D)

Only `1`

Solution:

Mass of a particular amount of substance is the amount of matter present in it. It is the inherent property of the substance and does not depend on location of the substance. Therefore, mass of the substance is independent of gravitational force between them.
Correct Answer is `=>` (B) `1` and `2`
Q 3151134024


NDA Paper 2 2015

Assertion : A body weighs less on a hill top than on the Earth's surface e\'en though its mass remains unchanged.

Reason : The acceleration clue to gravity of the Earth decreases with height.

(A) Both A and R individually true and R is the correct explanation of A
(B) Both A and R are individually true but R is not the correct explanation of A
(C) A is true but R is false
(D) A is false but R is true
Solution:

Mass of a particular amount of substance is the amount of matter present in it. It is the inherent property of the substance and does not depend on location of the substance. Therefore, mass of the substance is independent of gravitational force between them.
Correct Answer is `=>` (A)
Q 1608145008

If radius of the Earth were to shrink by `1%` , its mass remaining the same, `g` would decrease by nearly
NDA Paper 2 2015
(A)

`1%`

(B)

`2%`

(C)

`3%`

(D)

`4%`

Solution:

Mass of a particular amount of substance is the amount of matter present in it. It is the inherent property of the substance and does not depend on location of the substance. Therefore, mass of the substance is independent of gravitational force between them.
Correct Answer is `=>` (C) `3%`
Q 1649301213

The radius of the Moon is about one-fourth that of the Earth and acceleration due to gravity on the Moon is about one-sixth that on the Earth. From this, we can conclude that the ratio of the mass of the Earth to the mass of the Moon is about
NDA Paper 2 2015
(A)

10

(B)

100

(C)

1000

(D)

10000

Solution:

The mass of the Earth, `M_e = (9R_e^2)/G`

The mass of the Moon, `M_m = ( g'R_m^2)/G`

`:. (M_e)/(M_m) = ( gR_m^2)/( gR_m^2) = g/(g//6) xx R^2/(R_m/4)^2`

` (M_e)/(M_m) = 96 approx 100`
Correct Answer is `=>` (B) 100
Q 1616056879

The acceleration due to gravity `'g'` for objects on or near the surface of Earth is related to the universal gravitational constant 'G' as ('M' is the mass of the Earth and 'R' is its radius)
NDA Paper 2 2015
(A)

` G = g M/R^2`

(B)

` g = G M/R^2`

(C)

` M = (gG)/R^2`

(D)

` R = (gG)/M^2`

Solution:

The acceleration due to gravity can be derived from law of gravitation. i.e. Gravitational force between mass of Earth (M) and a body of mass (m) is given by `F = (GMm)/R^2 ` `quad` [R =Radius of Earth] ... (i) Again, we know Earth attracts anybody with the force ` F = m xx g` ... (ii) From F::qs. (i) and (ii), WE! get ` (GMm)/R^2 = mg => g = (GM)/R^2`
Correct Answer is `=>` (B) ` g = G M/R^2`
Q 1713801749

The question consist of two statements, text(Statement I) and text(Statement II). You are to examine these two statements carefully and select the answer.

`text(Statement I)` The acceleration due to gravity decreases with increase in height from the surface of the Earth.
`text(Statement II)` The acceleration due to gravity is inversely
proportional to the square of the distance from the centre of the Earth.
NDA Paper 2 2014
(A)

Both the statements are individually true and Statement 2. is the correct explanation of Statement 1

(B)

Both the statements are individually true, but Statement 2 is not the correct explanation of Statement 1

(C)

Statement 1 is true, but Statement 2 is false

(D)

Statement 1 is the false, but statement 2 is true

Solution:

The acceleration due to gravity can be derived from law of gravitation. i.e. Gravitational force between mass of Earth (M) and a body of mass (m) is given by `F = (GMm)/R^2 ` `quad` [R =Radius of Earth] ... (i) Again, we know Earth attracts anybody with the force ` F = m xx g` ... (ii) From F::qs. (i) and (ii), WE! get ` (GMm)/R^2 = mg => g = (GM)/R^2`
Correct Answer is `=>` (A) Both the statements are individually true and Statement 2. is the correct explanation of Statement 1
Q 1763767645

Planet A has double the radius than that of Planet `B`. If the mass of Planet `A` is `4` times heavier than the mass of Planet `B`, which of the following statements regarding weight of an object is correct?
NDA Paper 2 2014
(A)

Heavier on Planet A than on Planet B

(B)

Heavier on Planet B than on Planet A

(C)

Same on both the planets

(D)

Cannot be measured on Planet B

Solution:

The acceleration due to gravity can be derived from law of gravitation. i.e. Gravitational force between mass of Earth (M) and a body of mass (m) is given by `F = (GMm)/R^2 ` `quad` [R =Radius of Earth] ... (i) Again, we know Earth attracts anybody with the force ` F = m xx g` ... (ii) From F::qs. (i) and (ii), WE! get ` (GMm)/R^2 = mg => g = (GM)/R^2`
Correct Answer is `=>` (C) Same on both the planets
Q 1741767623

If the length of the Equator is about 40000 km and the velocity of rotation is about 1700 km per hour, what would be the velocity of rotation at the pole?
NDA Paper 2 2014
(A)

Zero

(B)

850 km/h

(C)

1700 km/h

(D)

3400 km/h

Solution:

Using `V_e = R_eW`

`1700 km//h = 20000 xx W`

`W =( 1700)/(20000) = (17)/(200)` rotation/hour

Velocity of rotation at pole,

` V_p = R_p`

as `R_p = 0 => V_p = 0`
Correct Answer is `=>` (A) Zero
Q 2314434350

Gravitational force shares a common feature with electromagnetic force. In both cases, the force is.
NDA Paper 2 2013
(A)

between massive and neutral objects

(B)

between charged objects

(C)

a short range

(D)

a long range

Solution:

Gravitational force shares a common feature with electromagnetic force. In both cases, the force is between massive and neutral objects.
Correct Answer is `=>` (A) between massive and neutral objects
Q 2313067849

The weight of an object may be assigned using Newton's
NDA Paper 2 2013
(A)

first law of motion

(B)

second law of motion

(C)

third law of motion

(D)

laws of gravitation

Solution:

Newton's law of universal gravitation states that every
point mass in the universe attracts every other point mass with a
force that is directly proportional to the product of their masses
and inversely proportional to the square of the distance between
them.

`F=G(m_1 m_2)/r^2`

where, `F =` Force between the masses
`G =` Gravitational constant
`m_1 =` First mass
`m _2 =` Second mass
`r =` Distance between the centre of the masses
Correct Answer is `=>` (D) laws of gravitation
Q 2363578445

A piece of paper and a coin both having the same mass are dropped from the `10th` floor a building. The piece of paper would take more time to reach the ground because.
NDA Paper 2 2013
(A)

gravitational pull on the paper is less than the coin

(B)

buoyant force on the piece of paper is more than that on the coin

(C)

buoyant force on the coin is more and acts in the downward direction

(D)

the piece of paper takes a longer path to reach the ground

Solution:

The piece of paper would take more time to reach the
ground than a coin because boyance force on the piece of paper
is more than that on the coin
Correct Answer is `=>` (B) buoyant force on the piece of paper is more than that on the coin
Q 2374645556

One feels heavier in a lift when the lift
NDA Paper 2 2012
(A)

is going down steadily

(B)

just begins to go up

(C)

is moving up steadily

(D)

descends freely

Solution:

One feels heavier in a lift when the lift just begins to go up.
Correct Answer is `=>` (B) just begins to go up
Q 2324356251

A body weighs `5` kg on equator. At the poles, it is likely to weigh
NDA Paper 2 2012
(A)

5 kg

(B)

less than 5 kg but not zero

(C)

0 kg

(D)

more than 5 kg

Solution:

If body weighs 5 kg on equator, at the poles it is likely to weigh more than 5 kg it due to centrifugal force spinning lowers the body weight by about 0.4% at the equator relative to its weight at the poles.
Correct Answer is `=>` (D) more than 5 kg
Q 2354580454

A body attached to a spring balance weighs `10` kg on the Earth. The body attached to the same spring balance is taken to a planet where gravity is half that of the Earth. The spring balance will read
NDA Paper 2 2012
(A)

`20` kg

(B)

`10` kg

(C)

`5` kg

(D)

`2.5` kg

Solution:

If body weighs 5 kg on equator, at the poles it is likely to weigh more than 5 kg it due to centrifugal force spinning lowers the body weight by about 0.4% at the equator relative to its weight at the poles.
Correct Answer is `=>` (C) `5` kg
Q 2324080851

Which one among the following is the correct value of the gravitational force of the Earth acting on a body of mass `1` kg?
NDA Paper 2 2011
(A)

`8.9` N

(B)

`9.8` N

(C)

`89` N

(D)

`98` N

Solution:

Gravitational force of the Earth, `F = mg`

Given, `m = 1` kg

`:. F=1 xx 98 kg-m//s^2`

`=9.8 N`
Correct Answer is `=>` (B) `9.8` N
Q 2375156966

An annular solar eclipse occurred during January 2010 with duration of annularity around `12` min. It is predicted that such long annular duration will not occur till the year `3043`. Such prediction is possible due to
NDA Paper 2 2010
(A)

Einstein's theory of relativity

(B)

Darwin's theory of natural selection

(C)

Newton's theory of gravitation

(D)

Hawking's theory of black hole

Solution:

The predictions of solar and lunar eclipses can be done by the help of Newton's law of gravitation.
Correct Answer is `=>` (C) Newton's theory of gravitation
Q 2346112973


NDA Paper 2 2009

Assertion : Two artificial satellite having different masses and revolving around the Earth in the same circular orbit have same speed.

Reason : The speed of a satellite is directly proportional to the radius of its orbit.

(A) Both A and R individually true and R is the correct explanation of A
(B) Both A and R are individually true but R is not the correct explanation of A
(C) A is true but R is false
(D) A is false but R is true
Solution:

Orbital velocity is indepenclent of the mass of the
orbiting body and is always along the tangent to the orbit, i.e.,
satellite of different masses have same orbital velocity, if they are
in the same orbit. For a given planet `v prop 1/sqrt r` Only Assertion is
correct.
Correct Answer is `=>` (C)
 
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