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Let, $E_{1}$ and $E_{2}$ denotes gravitational field at distance $r_{1}$ and $r_{2}$ from the axis of an infinitely long solid cylinder of radius $R$ . Which of the following must hold true?

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Important Questions on Gravitation

HARD

Physics>Mechanics>Gravitation>Acceleration Due To Gravity

The mass density of a spherical body is given by

ρ (r) = \frac{k}{r}

for

r \leq R

and

ρ (r) = 0

for

r > R,

where

r

is the distance from the center. The correct graph that describes qualitatively the acceleration,

a

of a test particle as a function of

r

is:

MEDIUM

Physics>Mechanics>Gravitation>Acceleration Due To Gravity

A ball is launched from the top of Mount Everest which is at an elevation of

9000 m

. The ball moves in a circular orbit around the earth. The acceleration due to gravity near the earth's surface is

g

. The magnitude of the ball's acceleration while in orbit is,

MEDIUM

Physics>Mechanics>Gravitation>Acceleration Due To Gravity

If the Earth has no rotational motion, the weight of a person on the equator is

W

. Determine the speed with which the earth would have to rotate about its axis so that the person at the equator will weigh

\frac{3}{4} W

. The radius of the Earth is

6400 km

and

g = 10 m s^{- 2}

EASY

Physics>Mechanics>Gravitation>Acceleration Due To Gravity

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

)

EASY

Physics>Mechanics>Gravitation>Acceleration Due To Gravity

Suppose that the angular velocity of rotation of the Earth is increased. Then, as a consequence,

EASY

Physics>Mechanics>Gravitation>Acceleration Due To Gravity

The acceleration due to gravity at a height

1 km

above the earth is the same as at a depth

d

below the surface of earth. Then

EASY

Physics>Mechanics>Gravitation>Acceleration Due To Gravity

Two planets

A

and

B

have the same average density. Their radii

R_{A}

and

R_{B}

are such that

R_{A} : R_{B} = 3 : 1

. If

g_{A}

and

g_{B}

are the acceleration due to gravity at the surfaces of the planets, the

g_{A} : g_{B}

equals

MEDIUM

Physics>Mechanics>Gravitation>Acceleration Due To Gravity

The ratio of the weight of a body at a height of

\frac{R}{10}

from the surface of the earth to that at a depth of

\frac{R}{10}

is (

R

is radius of earth)

EASY

Physics>Mechanics>Gravitation>Acceleration Due To Gravity

Starting from the center of the earth having radius,

R

, the variation of

g

(acceleration due to gravity) is shown by

EASY

Physics>Mechanics>Gravitation>Acceleration Due To Gravity

The variation of acceleration due to gravity

g

with distance

d

from the centre of the earth is best represented by (

R

= Earth's radius):

EASY

Physics>Mechanics>Gravitation>Acceleration Due To Gravity

Dependence of intensity of gravitational field

(E)

of earth with distance

(r)

from centre of earth is correctly represented by:

EASY

Physics>Mechanics>Gravitation>Acceleration Due To Gravity

If the change in the value of

g

at a height

h

above the surface of the earth is the same as at a depth

x

below it, then (both

x

and

h

being much smaller than the radius of the earth)

EASY

Physics>Mechanics>Gravitation>Acceleration Due To Gravity

A solid sphere of mass

M

and radius

a

is surrounded by a uniform concentric spherical shell of thickness

2 a

and mass

2 M .

The gravitational field at distance

3 a

from the centre will be:

HARD

Physics>Mechanics>Gravitation>Acceleration Due To Gravity

A plank is resting on a horizontal ground in the northern hemisphere of the Earth at a

45^{o}

latitude. Let the angular speed of the Earth be

ω

and its radius

r_{e}

. The magnitude of the frictional force on the plank will be

MEDIUM

Physics>Mechanics>Gravitation>Acceleration Due To Gravity

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 {m s}^{- 2}

at the north pole and the radius of the earth

= 6400 k m

EASY

Physics>Mechanics>Gravitation>Acceleration Due To Gravity

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)

MEDIUM

Physics>Mechanics>Gravitation>Acceleration Due To Gravity

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)

MEDIUM

Physics>Mechanics>Gravitation>Acceleration Due To Gravity

The depth

d

at which the value of acceleration due to gravity becomes

\frac{1}{n}

times the value at the earth's surface is

(R

= radius of the earth

)

HARD

Physics>Mechanics>Gravitation>Acceleration Due To Gravity

A very long (length $L$ ) cylindrical galaxy is made of uniformly distributed mass and has radius $R (R < < L)$ . A star outside the galaxy is orbiting the galaxy in a plane perpendicular to the galaxy and passing through its centre. If the time period of the star is $T$ and its distance from the galaxy's axis is $r$ , then

EASY

Physics>Mechanics>Gravitation>Acceleration Due To Gravity

At what height from the surface of earth the gravitation potential and the value of g are

- 5.4 \times 10^{7} J k g^{- 2}

and

6.0 m s^{- 2}

respectively? Take the radius of earth as

6400 km

Let, E1 and E2 denotes gravitational field at distance r1 and r2 from the axis of an infinitely long solid cylinder of radius R. Which of the following must hold true?

Important Questions on Gravitation

Learn and Prepare for any exam you want !

Let, $E_{1}$ and $E_{2}$ denotes gravitational field at distance $r_{1}$ and $r_{2}$ from the axis of an infinitely long solid cylinder of radius $R$ . Which of the following must hold true?