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Which of the following statements are true about acceleration due to gravity?

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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:

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 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

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

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

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)

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

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

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

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)

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 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?

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

MEDIUM

Physics>Mechanics>Gravitation>Acceleration Due To Gravity

What is the depth at which the value of acceleration due to gravity becomes

\frac{1}{n}

times the value at the surface of the earth? (radius of the earth

= R

)

MEDIUM

Physics>Mechanics>Gravitation>Acceleration Due To Gravity

A stone weighs

100 N

on the surface of the Earth. The ratio of its weight at a height of half the radius of the Earth to a depth of half the radius of the earth will be approximately

MEDIUM

Physics>Mechanics>Gravitation>Acceleration Due To Gravity

Which of the following graphs correctly represents the variation of

' g'

on the Earth?

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

Which of the following statements are true about acceleration due to gravity?

Important Questions on Gravitation

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