HARD

Earn 100

Discuss the variation of $g$ with latitude.

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

Discuss the variation of g with latitude.

Important Questions on Gravitation

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Discuss the variation of $g$ with latitude.