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NEET • PHYSICS • GRAVITATION

Gravitation practice · Hard

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1 Hard

1 of 21

Application +4 | -1

If potential energy is given by

\mathrm{U}=\frac{\mathrm{a}}{\mathrm{r}^2}-\frac{\mathrm{b}}{\mathrm{r}}

. Then find out maximum force. (given

\mathrm{a=2, b}=4

)

View answer and explanation

Correct option: A

-\frac{16}{27} \mathrm{~N}

Option A (

-\frac{16}{27} \mathrm{~N}

) is correct because it represents the maximum force calculated by finding the point where the derivative of the force function is zero.

2 Hard

2 of 21

Application +4 | -1

An artificial satellite is moving in a circular orbit around the earth with a speed equal to half the magnitude of escape velocity from the earth. If the satellite is stopped in its orbit and allowed to fall freely onto the earth, the speed with which it hits the surface _____

\mathrm{km} / \mathrm{s}.

[g=

9.8 \mathrm{~ms}^{-2}

and

\left.{R}_e=6400 \mathrm{~km}\right]

View answer and explanation

Correct option: A

7.92

Option A (T) is correct because the period depends on the density of the planet, and since the density is the same, the period remains the same.

3 Hard

3 of 21

Application +4 | -1

A body of mass

m

is projected with a velocity of

\frac{1}{\sqrt{2}}

times the escape velocity from the surface of earth in the vertical upward direction. If the air resistance is negligible, then the maximum distance of the body from is surface of earth is

x R

where

R

is the radius of earth. Find

x

View answer and explanation

Correct option: A

Option A (1) is correct because the maximum distance from the Earth's center is 2R, making the distance from the surface R, hence x=1.

4 Hard

4 of 21

Application +4 | -1

If an object is having same weight at same distance above and below the surface of earth, find its distance from surface of earth.

View answer and explanation

Correct option: B

(\sqrt{5}-1) \frac{R}{2}

Option B (

(\sqrt{5}-1) \frac{R}{2}

) is correct because it involves equating the gravitational acceleration at a height h and depth d and solving for h.

5 Hard

5 of 21

Analyzing +4 | -1

Given below are two statements: one is labelled as Assertion (A) and the other is labelled as Reason (R).

Assertion (A): Angular momentum conservation can be used to explain Kepler's second law of planetary motion.

Reason (R): Areal velocity of a planet revolving around the sun is equal to its angular momentum.

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

View answer and explanation

Correct option: C

(A) is true but (R) is false

Option C ((A) is true but (R) is false) is correct because angular momentum is conserved, but areal velocity is related to angular momentum per unit mass, not just angular momentum.

6 Hard

6 of 21

Application +4 | -1

A particle would take a time

t

to move down a straight tube from the surface of earth (supposed to be a homogeneous sphere) to its centre. If gravity were to remain constant, then the time would be

t

. The ratio of

t / t^{\prime}

will be

View answer and explanation

Correct option: C

\sqrt{2} \pi

Option C (

\sqrt{2} \pi

) is correct because it represents the ratio of time taken to travel through a tube to the center of the earth under varying and constant gravity conditions.

7 Hard

7 of 21

Application +4 | -1

Two planets, A and B are orbiting a common star in circular orbits of radii

\mathrm{R_A}

and

\mathrm{R_B},

respectively, with

\mathrm{R_B=2 R_A}.

The planet B is

4 \sqrt{2}

times more massive than planet A. The ratio

\mathrm{\left(\frac{L_B}{L_A}\right)}

of angular momentum

\left(\mathrm{L_B}\right)

of planet B to that of planet

\mathrm{A\left(L_A\right)}

is closest to integer ______

View answer and explanation

Correct option: A

Option A (8) is correct because the ratio of angular momenta is calculated using the given mass and radius relationship, resulting in an integer value of 8.

8 Hard

8 of 21

Analyzing +4 | -1

An artificial satellite of mass

m

of a planet (radius

R

, mass

{M})

revolves in a circular orbit whose orbital radius in

n

times the radius of the planet. In the process of motion, the satellite experiences a slight resistance due to cosmic dust. Assuming the resistive force

{F}={kv}^2

, where

{k}

is a constant and

v

the instantaneous velocity. The time taken by the satellite to fall from its orbit to the surface of the planet is found

\frac{m}{k} \sqrt{\frac{R}{G m}}(y \sqrt{n}-1)

. Find

y

View answer and explanation

Correct option: A

Option A (1) is correct because the time taken for the satellite to fall is derived from the resistive force and orbital mechanics, leading to y=1.

9 Hard

9 of 21

Analyzing +4 | -1

A double star consists of two stars having masses

M

and

2 M

. The distance between their centres is equal to

r

. They revolve under their mutual gravitational interaction. Then, which of the following statement(s) is/are correct?

View answer and explanation

Correct option: B

Both of the stars revolve with the same period which is equal to

\frac{2 \pi}{\sqrt{2 G M / 3}} r^{3 / 2}

Option B (Both of the stars revolve with the same period which is equal to

\frac{2 \pi}{\sqrt{2 G M / 3}} r^{3 / 2}

) is correct because the stars revolve around their center of mass with the same period, and the period can be calculated using Kepler's third law.

10 Hard

10 of 21

Application +4 | -1

An astronaut takes a ball of mass

m

from earth to space. He throws the ball into a circular orbit about earth at an altitude of

318.5 \mathrm{~km}

. From earth's surface to the orbit, the change in total mechanical energy of the ball is

x \frac{G M_e m}{21 R_e}

. The value of

x

is (take

\left.{R}_{{e}}=6370 \mathrm{~km}\right)

View answer and explanation

Correct option: A

Option A (11) is correct because the change in total mechanical energy is calculated by considering the change in potential and kinetic energy from the Earth's surface to the orbit.

11 Hard

11 of 21

Application +4 | -1

A body is projected vertically upwards from the surface of Earth with a velocity sufficient enough to carry it to infinity. The time taken by it to each height

h

is.......s.

View answer and explanation

Correct option: D

\frac{1}{3}\sqrt {\frac{{2{R_e}}}{g}} \left[ {{{\left( {1 + \frac{h}{{{R_e}}}} \right)}^{3/2}} - 1} \right]

Option D (

\frac{1}{3}\sqrt {\frac{{2{R_e}}}{g}} \left[ {{{{({1 + \frac{h}{{{R_e}}}})}^{3/2}} - 1} \right]

) is correct because it represents the time taken to reach height h when projected with escape velocity, derived from energy conservation and integration.

12 Hard

12 of 21

Remembering +4 | -1

Weight of body is maximum at:

View answer and explanation

Correct option: B

Poles of the earth

Option B (Poles of the earth) is correct because the acceleration due to gravity is maximum at the poles, leading to maximum weight.

13 Hard

13 of 21

Application +4 | -1

A projectile is fired upwards from the surface of the earth with a velocity

k{V_e}

where

{V_e}

is the escape and

K < 1

. If r is the maximum distance from the center of the earth to which it rises and R is the radius of the earth then r equals

View answer and explanation

Correct option: B

\frac{R}{{1 - {k^2}}}

Option B (

\frac{R}{{1 - {k^2}}}

) is correct because it is derived from the conservation of energy, relating the initial kinetic energy to the final potential energy at the maximum distance.

14 Hard

14 of 21

Application +4 | -1

A particle of mass

m

was transferred from infinity into the centre of the base of a uniform hemisphere of mass

M

and radius

R.

What work was performed in the process by the gravitational force exerted on the particle by the hemisphere?

View answer and explanation

Correct option: B

\frac{3 G m M}{2 R}

Option B (

\frac{{3 G m M}}{{{2 R}}}

) is correct because it represents the work done by gravity in bringing the particle from infinity to the center of the hemisphere's base.

15 Hard

15 of 21

Understanding +4 | -1

Assertion: Work done by or against gravitational force in moving a body from one point to another is independent of the actual path followed between the two points.
Reason: Gravitational forces are conservative forces.

View answer and explanation

Correct option: A

If both Assertion and Reason are true and Reason is the correct explanation of Assertion

Option A (If both Assertion and Reason are true and Reason is the correct explanation of Assertion) is correct because the assertion is true, the reason is true, and the reason correctly explains the assertion.

Explore Other Chapters in PHYSICS

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16 Hard

16 of 21

Understanding +4 | -1

An astronaut floating weightlessly in space shakes a large iron block rapidly back and forth. She compares that to her moving it on earth on a smooth horizontal surface. She find that:

View answer and explanation

Correct option: C

Although weightless, the effort required is same

Option C (Although weightless, the effort required is same) is correct. Inertia is independent of gravity; the astronaut still has to overcome the block's mass.

17 Hard

17 of 21

Application +4 | -1

Two planets

A

and

B

having masses

m_1

and

m_2

move around the sun in circular orbits of

r_1

and

r_2

radii respectively. If angular momentum of

\mathrm{A}

{L}

and that of

B

3 L

, the ratio of time period

\left(\frac{T_A}{T_B}\right)

is:

View answer and explanation

Correct option: C

\frac{1}{27}\left(\frac{m_2}{m_1}\right)^3

Option A (

\frac{1}{R}

) is correct because the kinetic energy of a satellite is inversely proportional to the radius of its orbit.

18 Hard

18 of 21

Application +4 | -1

The minimum energy required to launch a satellite of mass

m

from the surface of earth of mass

M

and radius

R

in a circular orbit at an altitude of

2 R

from the surface of the earth is:

View answer and explanation

Correct option: D

\frac{5 G m M}{6 R}

Option D (

\frac{{5 G m M}}{{{6 R}}}

) is correct because it represents the difference between the final energy in orbit and the initial potential energy on the Earth's surface.

19 Hard

19 of 21

Application +4 | -1

Mars has a diameter of approximately 0.5 of that of Earth and mass of 0.1 of that of Earth. The surface gravitational field strength on Mars as compared to that on Earth is greater by a factor of

View answer and explanation

Correct option: D

0.4

Option D (0.4) is correct because it correctly calculates the ratio of gravitational field strength on Mars to that on Earth.

20 Hard

20 of 21

Application +4 | -1

A rectangular plank of mass

{m_1}

and height a is kept on a horizontal surface. Another rectangular plank of mass

{m_2}

and height b is placed over the first plank. The gravitational potential energy of the system is

View answer and explanation

Correct option: C

\left[ {\left( {\frac{{{m_1}}}{2} + {m_2}} \right)a + {m_2}\frac{b}{2}} \right]

Option C (

\left[ {\frac{{{m_1}}}{2} + {m_2}} \right]a + {m_2}\frac{b}{2}

) is correct because it correctly sums the potential energies of both planks relative to the ground.

21 Hard

21 of 21

Analyzing +4 | -1

Pertaining to two planets, the ratio of escape velocities from respective surfaces is

1: 2

, the ratio of the time period of the same simple pendulum at their respective surfaces is

2: 1

(in same order). Then the ratio of their average densities is

View answer and explanation

Correct option: C

1: 4

Option C is correct. Given the ratio of escape velocities and time periods, we can derive the ratio of their average densities using the formulas for escape velocity and the time period of a simple pendulum.

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Key Takeaways

✓ This set contains 21 single-correct-answer MCQs on GRAVITATION.
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