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If the diameter of earth becomes half(mass remains unchanged), then the acceleration due to gravity at surface of earth becomes

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Important Questions on Gravitation

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

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

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

The value of the acceleration due to gravity is

g_{1}

at a height

h = \frac{R}{2}

(

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 the earth. The ratio

(\frac{d}{R})

equals:

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):

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)

EASY

Physics>Mechanics>Gravitation>Acceleration Due To Gravity

A body weighs

200 N

on the surface of the earth. How much will it weigh half way down to the centre of the earth?

HARD

Physics>Mechanics>Gravitation>Acceleration Due To Gravity

The ratio of accelerations due to gravity

g_{1} : g_{2}

on the surfaces of two planets is

5 : 2

and the ratio of their respective average densities

ρ_{1} : ρ_{2}

2 : 1 .

What is the ratio of respective escape velocities

v_{1} : v_{2}

from the surface of the planets?

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

)

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,

EASY

Physics>Mechanics>Gravitation>Acceleration Due To Gravity

A body weighs

72 N

on the surface of the earth. What is the gravitational force on it, at a height equal to half the radius of the earth?

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

The value of acceleration due to gravity at a height of

10 km

from the surface of earth is

x

. At what depth inside the earth is the value of the acceleration due to gravity has the same value

x

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:

MEDIUM

Physics>Mechanics>Gravitation>Acceleration Due To Gravity

The ratio of the height above the surface of earth to the depth below the surface of earth, for gravitational accelerations to be the same (assuming small heights), is

MEDIUM

Physics>Mechanics>Gravitation>Acceleration Due To Gravity

Which of the following graphs correctly represents the variation of

' g'

on the Earth?

HARD

Physics>Mechanics>Gravitation>Acceleration Due To Gravity

A spiral galaxy can be approximated as an infinitesimally thin disc of a uniform surface mass density (mass per unit area) located at

z = 0,

Two stars

A

and

B

start from rest from heights

2 z_{0}

and

z_{0}

(

z_{0} < <

radial extent of the disc), respectively and fall towards the disc, cross over to the other side and execute periodic oscillations. The ratio of time periods of

A

and

B

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:

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

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

If the diameter of earth becomes half(mass remains unchanged), then the acceleration due to gravity at surface of earth becomes

Important Questions on Gravitation

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