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Determine the average density of the planet for which the length of day is $6 hrs$ . When we weigh a body using spring balance at its equator, the scale shows weight $10 %$ less weight than that at the pole. Fill $\frac{ρ}{10^{4}}$ in $kg m^{- 3}$ in OMR sheet.

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Important Questions on Gravitation

MEDIUM

Physics>Mechanics>Gravitation>Acceleration Due to Gravity

In the reported figure of earth, the value of acceleration due to gravity is same at point $A$ and $C$ but it is smaller than that of its value at point $B$ (surface of the earth). The value of $O A : A B$ will be $x : 5$ . The value of $x$ is

Question Image

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?

EASY

Physics>Mechanics>Gravitation>Acceleration Due to Gravity

The gravitational field strength at the surface of a certain planet is

g .

Which of the following is the gravitational field strength at the surface of a planet with twice the radius and twice the mass?

MEDIUM

Physics>Mechanics>Gravitation>Acceleration Due to Gravity

The earth's mass is

80

times that of moon and their diameters are

1600 km

and

800 km

, respectively. If

g

is the value of acceleration due to gravity on earth, what is its value on moon?

HARD

Physics>Mechanics>Gravitation>Acceleration Due to Gravity

A spherical body of radius

R

consists of a fluid of constant density and is in equilibrium under its own gravity. If

P (r)

is the pressure at

r (r < R)

, then the correct option(s) is (are)

HARD

Physics>Mechanics>Gravitation>Acceleration Due to Gravity

Consider a planet in some solar system that has a mass double the mass of earth and density equal to the average density of the earth. If the weight of an object on earth is

W

, the weight of the same object on that planet will be:

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

EASY

Physics>Mechanics>Gravitation>Acceleration Due to Gravity

A body of mass

60 g

experiences a gravitational force of

3.0 N

, when placed at a particular point. The magnitude of the gravitational field intensity at that point is

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

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

Infinite number of masses each of

3 kg

are placed along a straight line at the distances of

1 m

2 m, 4 m, 8 m, \dots \dots

from a point

0

on the same line. If

G

is the universal gravitational constant, then the magnitude of gravitational field intensity at

0

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

A body weighs $900 gm .$ wt on the surface of the earth. Its weight on the surface of a planet whose mass is $\frac{1}{8}$ ^th of that of the earth and radius is half that of the earth, is

EASY

Physics>Mechanics>Gravitation>Acceleration Due to Gravity

Imagine a new planet having the same density as that of the earth but it is

3

times bigger than the earth in size. If the acceleration due to gravity on the surface of the earth is

g

and on the surface of the new planet is

g^{'}

, then

MEDIUM

Physics>Mechanics>Gravitation>Acceleration Due to Gravity

The elongation of a wire on the surface of the earth is

10^{- 4} m

. The same wire of same dimensions is elongated by

6 \times 10^{- 5} m

on another planet. The acceleration due to gravity on the planet will be _____

m s^{- 2}

. (Take acceleration due to gravity on the surface of earth

= 10 {m s}^{- 2}

)

EASY

Physics>Mechanics>Gravitation>Acceleration Due to Gravity

A planet has double the mass of the earth. Its average density is equal to that of the earth. An object weighing $W$ on earth will weigh on that planet:

EASY

Physics>Mechanics>Gravitation>Acceleration Due to Gravity

If the radius of earth shrinks by

2 %

while its mass remains same. The acceleration due to gravity on the earth's surface will approximately

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

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,

Determine the average density of the planet for which the length of day is 6 hrs. When we weigh a body using spring balance at its equator, the scale shows weight 10% less weight than that at the pole. Fill ρ104 in kg m-3 in OMR sheet.

Important Questions on Gravitation

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Determine the average density of the planet for which the length of day is $6 hrs$ . When we weigh a body using spring balance at its equator, the scale shows weight $10 %$ less weight than that at the pole. Fill $\frac{ρ}{10^{4}}$ in $kg m^{- 3}$ in OMR sheet.