Given below are two statements : 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

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

Statement I is false but Statement II is true

HARD

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IMPORTANT

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A test particle is moving in a circular orbit in the gravitational field produced by a mass density $ρ (r) = \frac{K}{r^{2}} .$ Identify the current relation between the radius $R$ of the particle’s orbit and its period $T :$

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Important Questions on Gravitation

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EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR PHYSICS>Chapter 6 - Gravitation>JEE Main - 9th January 2019 Shift 1>Q 51

If the angular momentum of a planet of mass

m,

moving around the Sun in a circular orbit is

L,

about the center of the Sun, its areal velocity is:

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EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR PHYSICS>Chapter 6 - Gravitation>JEE Main - 9th January 2019 Shift 2>Q 52

The energy required to take a satellite to a height

h

above the Earth surface (radius of Earth

= 6.4 \times 10^{3} km

) is

E_{1}

, and the kinetic energy required for the satellite to be in a circular orbit at this height is

E_{2} .

The value of

h

for which

E_{1}

and

E_{2}

are equal, is

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EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR PHYSICS>Chapter 6 - Gravitation>JEE Main - 8th April 2019 Shift 1>Q 53

Four identical particles of mass $M$ are located at the corners of a square of side $‘ a ’$ . What should be their speed if each of them revolves under the influence of other’s gravitational field in a circular orbit circumscribing the square?
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EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR PHYSICS>Chapter 6 - Gravitation>JEE Main - 8th April 2019 Shift 2>Q 54

A rocket has to be launched from earth in such a way that it never returns. If

E

is the minimum energy delivered by the rocket launcher, what should be the minimum energy that the launcher should have, if the same rocket is to be launched from the surface of the moon? Assume that the density of the earth and the moon are equal and that the earth's volume is

64

times the volume of the moon.

EASY

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EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR PHYSICS>Chapter 6 - Gravitation>JEE Main - 10th April 2019 Shift 1>Q 55

The value of acceleration due to gravity at Earth's surface is

9.8 m s^{- 2}

. The altitude above its surface at which the acceleration due to gravity decreases to

4.9 m s^{- 2}

, is close to: (Radius of earth

= 6.4 \times 10^{6} m

)

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EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR PHYSICS>Chapter 6 - Gravitation>JEE Main - 10th April 2019 Shift 2>Q 56

A spaceship orbits around a planet at a height of

20 k m

from its surface. Assuming that only gravitational field of the planet acts on the spaceship, what will be the number of complete revolutions made by the spaceship in

24

hours around the planet?
[Given: Mass of planet

= 8 \times 10^{22} k g

,
Radius of planet

= 2 \times 10^{6} m,

Gravitational constant

G = 6.67 \times 10^{- 11} N m^{2} / k g^{2}

]

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EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR PHYSICS>Chapter 6 - Gravitation>JEE Main - 10th January 2019 Shift 1>Q 57

A satellite is moving with a constant speed

v

in circular orbit around the earth. An object of mass 'm' is ejected from the satellite such that it just escapes from the gravitational pull of the earth. At the time of ejection, the kinetic energy of the object is:

HARD

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IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR PHYSICS>Chapter 6 - Gravitation>JEE Main - 10th January 2019 Shift 2>Q 58

Two stars of masses

3 \times 10^{31} kg

each, and at distance

2 \times 10^{11} m

rotate in a plane about their common centre of mass

O .

A meteorite passes through

O

moving perpendicular to the star's rotation plane. In order to escape from the gravitational field of this double star, the minimum speed that meteorite should have at

O

is ( Take Gravitational constant

G = 6.67 \times 10^{- 11} N m^{2} {kg}^{- 2}

)

A test particle is moving in a circular orbit in the gravitational field produced by a mass density ρr=Kr2. Identify the current relation between the radius R of the particle’s orbit and its period T:

Important Questions on Gravitation

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A test particle is moving in a circular orbit in the gravitational field produced by a mass density $ρ (r) = \frac{K}{r^{2}} .$ Identify the current relation between the radius $R$ of the particle’s orbit and its period $T :$