# Gravitation Test 3

Total Questions:50 Total Time: 75 Min

Remaining:

## Questions 1 of 50

Question:A body weighs 700 gm wt on the surface of the earth. How much will it weigh on the surface of a planet whose mass is $$\frac{1}{7}$$ and radius is half that of the earth

200 gm wt

400 gm wt

50 gm wt

300 gm wt

## Questions 2 of 50

Question:In order to find time, the astronaut orbiting in an earth satellite should use

A pendulum clock

A watch having main spring to keep it going

Either a pendulum clock or a watch

Neither a pendulum clock nor a watch

## Questions 3 of 50

Question:A spherical planet far out in space has a mass $${M_0}$$ and diameter $${D_0}$$. A particle of mass m falling freely near the surface of this planet will experience an acceleration due to gravity which is equal to

$$G{M_0}/D_0^2$$

$$4mG{M_0}/D_0^2$$

$$4G{M_0}/D_0^2$$

$$Gm{M_0}/D_0^2$$

## Questions 4 of 50

Question:The value of g on the earth's surface is $$980\,cm/{\sec ^2}$$. Its value at a height of 64 km from the earth's surface is

$$960.40\,cm/{\sec ^2}$$

$$984.90\,cm/{\sec ^2}$$

$$982.45\,cm/{\sec ^2}$$

$$977.55\,cm/{\sec ^2}$$

## Questions 5 of 50

Question:Choose the correct statement from the following :Weightlessness of an astronaut moving in a satellite is a situation of

Zero g

No gravity

Zero mass

Free fall

## Questions 6 of 50

Question:If the earth rotates faster than its present speed, the weight of an object will

Increase at the equator but remain unchanged at the poles

Decrease at the equator but remain unchanged at the poles

Remain unchanged at the equator but decrease at the poles

Remain unchanged at the equator but increase at the poles

## Questions 7 of 50

Question:If the radius of the earth shrinks by 1.5% (mass remaining same), then the value of acceleration due to gravity changes by

1%

2%

3%

4%

## Questions 8 of 50

Question:If radius of the earth contracts 2% and its mass remains the same, then weight of the body at the earth surface

Will decrease

Will increase

Will remain the same

None of these

## Questions 9 of 50

Question:If mass of a body is M on the earth surface, then the mass of the same body on the moon surface is

M/6

Zero

M

None of these

## Questions 10 of 50

Question:The angular speed of earth, so that the object on equator may appear weightless, is $$(g = 10\,m/{s^2}$$, radius of earth 6400 km)

$$1.25 \times {10^{ - 3}}rad/sec$$

$$1.56 \times {10^{ - 3}}rad/sec$$

$$1.25 \times {10^{ - 1}}rad/sec$$

## Questions 11 of 50

Question:At what distance from the centre of the earth, the value of acceleration due to gravity g will be half that on the surface (R = radius of earth)

2 R

R

1.414 R

0.414 R

## Questions 12 of 50

Question:The depth at which the effective value of acceleration due to gravity is $$\frac{g}{4}$$ is

R

$$\frac{{3R}}{4}$$

$$11.2 \times {10^2}\,km{s^{ - 1}}$$

$$\frac{R}{4}$$

## Questions 13 of 50

Question:Weight of a body of mass m decreases by 1% when it is raised to height h above the earth’s surface. If the body is taken to a depth h in a mine, change in its weight is

2% decrease

0.5% decrease

1% increase

0.5% increase

## Questions 14 of 50

Question:If both the mass and the radius of the earth decrease by 1%, the value of the acceleration due to gravity will

Decrease by 1%

Increase by 1%

Increase by 2%

Remain unchanged

## Questions 15 of 50

Question:There are two bodies of masses 100 kg and 10000 kg separated by a distance 1 m. At what distance from the smaller body, the intensity of gravitational field will be zero

$$\frac{1}{9}m$$

$$\frac{1}{{10}}m$$

$$\frac{1}{{11}}m$$

$$\frac{{10}}{{11}}m$$

## Questions 16 of 50

Question:What is the intensity of gravitational field of the centre of a spherical shell

$$Gm/{r^2}$$

g

Zero

None of these

## Questions 17 of 50

Question:The gravitational potential energy of a body of mass ‘m’ at the earth’s surface $$- mg{R_e}$$. Its gravitational potential energy at a height $${R_e}$$ from the earth’s surface will be (Here $${R_e}$$ is the radius of the earth)

$$- 2\,mg{R_e}$$

$$2\,mg{R_e}$$

$$\frac{1}{2}mg{R_e}$$

$$- \frac{1}{2}mg{R_e}$$

## Questions 18 of 50

Question:The escape velocity from the earth is about 11 km/second. The escape velocity from a planet having twice the radius and the same mean density as the earth, is

22 km/sec

11 km/sec

5.5 km/sec

15.5 km/sec

## Questions 19 of 50

Question:A missile is launched with a velocity less than the escape velocity. The sum of its kinetic and potential energy is

Positive

Negative

Zero

May be positive or negative depending upon its initial velocity

## Questions 20 of 50

Question:If g is the acceleration due to gravity at the earth's surface and r is the radius of the earth, the escape velocity for the body to escape out of earth's gravitational field is

gr

$$\sqrt {2gr}$$

$$g/r$$

$$r/g$$

## Questions 21 of 50

Question:Given mass of the moon is 1/81 of the mass of the earth and corresponding radius is 1/4 of the earth. If escape velocity on the earth surface is 11.2 km/s, the value of same on the surface of the moon is

0.14 km/s

0.5 km/s

2.5 km/s

5 km/s

## Questions 22 of 50

Question:The angular velocity of rotation of star (of mass M and radius R) at which the matter start to escape from its equator will be

$$\sqrt {\frac{{2G{M^2}}}{R}}$$

$$\sqrt {\frac{{2GM}}{g}}$$

$$\sqrt {\frac{{2GM}}{{{R^3}}}}$$

$$\sqrt {\frac{{2GR}}{M}}$$

## Questions 23 of 50

Question:The escape velocity for the earth is $${v_e}$$. The escape velocity for a planet whose radius is four times and density is nine times that of the earth, is

$$36\,{v_e}$$

$$12\,{v_e}$$

$$6\,{v_e}$$

$$20\,{v_e}$$

## Questions 24 of 50

Question:The escape velocity for a body projected vertically upwards from the surface of earth is 11 km/s. If the body is projected at an angle of 45o with the vertical, the escape velocity will be

$$\frac{{11}}{{\sqrt 2 }}km/s$$

$$11\sqrt 2 \,km/s$$

22 km/s

11 km/s

## Questions 25 of 50

Question:If V, R and g denote respectively the escape velocity from the surface of the earth radius of the earth, and acceleration due to gravity, then the correct equation is

$$V = \sqrt {gR}$$

$$V = \sqrt {\frac{4}{3}g{R^3}}$$

$$V = R\sqrt g$$

$$V = \sqrt {2gR}$$

## Questions 26 of 50

Question:Two planets move around the sun. The periodic times and the mean radii of the orbits are $${T_1},\,{T_2}$$ and $${r_1},\,{r_2}$$ respectively. The ratio $${T_1}/{T_2}$$ is equal to

$${({r_1}/{r_2})^{1/2}}$$

$${r_1}/{r_2}$$

$${({r_1}/{r_2})^2}$$

$${({r_1}/{r_2})^{3/2}}$$

## Questions 27 of 50

Question:Kepler's second law regarding constancy of aerial velocity of a planet is a consequence of the law of conservation of

Energy

Angular momentum

Linear momentum

None of these

## Questions 28 of 50

Question:The maximum and minimum distances of a comet from the sun are $$8 \times {10^{12}}\,m$$ and $$1.6 \times {10^{12}}\,m$$. If its velocity when nearest to the sun is 60 m/s, what will be its velocity in m/s when it is farthest

12

60

112

6

## Questions 29 of 50

Question:A body revolved around the sun 27 times faster then the earth what is the ratio of their radii

3-Jan

9-Jan

27-Jan

4-Jan

## Questions 30 of 50

Question:The period of moon’s rotation around the earth is nearly 29 days. If moon’s mass were 2 fold, its present value and all other things remained unchanged, the period of moon’s rotation would be nearly

$$29\sqrt 2$$days

$$29/\sqrt 2$$ days

29 × 2 days

29 days

## Questions 31 of 50

Question:What does not change in the field of central force

Potential energy

Kinetic energy

Linear momentum

Angular momentum

## Questions 32 of 50

Question:The eccentricity of earth's orbit is 0.0167. The ratio of its maximum speed in its orbit to its minimum speed is

2.507

1.033

8.324

1

## Questions 33 of 50

Question:The mass of a planet that has a moon whose time period and orbital radius are T and R respectively can be written as

$$4{\pi ^2}{R^3}{G^{ - 1}}{T^{ - 2}}$$

$$8{\pi ^2}{R^3}{G^{ - 1}}{T^{ - 2}}$$

$$12{\pi ^2}{R^3}{G^{ - 1}}{T^{ - 2}}$$

$$16{\pi ^2}{R^3}{G^{ - 1}}{T^{ - 2}}$$

## Questions 34 of 50

Question:The period of a satellite in a circular orbit around a planet is independent of

The mass of the planet

The mass of the satellite

All the three parameters ,

1 and 2

## Questions 35 of 50

Question:If a satellite is orbiting the earth very close to its surface, then the orbital velocity mainly depends on

The mass of the satellite only

The radius of the earth only

The mass of the earth only

## Questions 36 of 50

Question:The relay satellite transmits the T.V. programme continuously from one part of the world to another because its

Period is greater than the period of rotation of the earth

Period is less than the period of rotation of the earth about its axis

Period has no relation with the period of the earth about its axis

Period is equal to the period of rotation of the earth about its axis

Mass is less than the mass of the earth

## Questions 37 of 50

Question:Two identical satellites are at R and 7R away from earth surface, the wrong statement is (R = Radius of earth)

Ratio of total energy will be 4

Ratio of kinetic energies will be 4

Ratio of potential energies will be 4

Ratio of total energy will be 4 but ratio of potential and kinetic energies will be 2

## Questions 38 of 50

Question:For a satellite escape velocity is 11 km/s. If the satellite is launched at an angle of $${\rm{6}}0^\circ$$ with the vertical, then escape velocity will be

11 km/s

$$11\sqrt 3$$ km/s

$$\frac{{11}}{{\sqrt 3 }}$$ km/s

33 km/s

## Questions 39 of 50

Question:Given radius of Earth ‘R’ and length of a day ‘T’ the height of a geostationary satellite is [G–Gravitational Constant, M–Mass of Earth]

$${\left( {\frac{{4{\pi ^2}GM}}{{{T^2}}}} \right)^{1/3}}$$

$${\left( {\frac{{4\pi GM}}{{{R^2}}}} \right)^{1/3}} - R$$

$${\left( {\frac{{GM{T^2}}}{{4{\pi ^2}}}} \right)^{1/3}} - R$$

$${\left( {\frac{{GM{T^2}}}{{4{\pi ^2}}}} \right)^{1/3}} + R$$

## Questions 40 of 50

Question:A geo-stationary satellite is orbiting the earth at a height of 6 R above the surface of earth, R being the radius of earth. The time period of another satellite at a height of 2.5 R from the surface of earth is

10 hr

$$(6/\sqrt 2 )\,hr$$

6 hr

$$6\sqrt 2 \,hr$$

## Questions 41 of 50

Question:The distance between centre of the earth and moon is 384000 km. If the mass of the earth is $$6 \times {10^{24}}kg$$ and $$G = 6.66 \times {10^{ - 11}}N{m^2}/k{g^2}$$. The speed of the moon is nearly

1 km/sec

4 km/sec

8 km/sec

11.2 km/sec

## Questions 42 of 50

Question:If satellite is shifted towards the earth. Then time period of satellite will be

Increase

Decrease

Unchanged

Nothing can be said

## Questions 43 of 50

Question:Which of the following quantities does not depend upon the orbital radius of the satellite

$$\frac{T}{R}$$

$$\frac{{{T^2}}}{R}$$

$$\frac{{{T^2}}}{{{R^2}}}$$

$$\frac{{{T^2}}}{{{R^3}}}$$

## Questions 44 of 50

Question:The time period of a satellite of earth is 5 hours. If the separation between the earth and the satellite is increased to four times the previous value, the new time period will become

20 hours

10 hours

80 hours

40 hours

## Questions 45 of 50

Question:The gravitational force between two stones of mass 1 kg each separated by a distance of 1 metre in vacuum is

Zero

$$6.675 \times {10^{ - 5}}\,newton$$

$$6.675 \times {10^{ - 11}}\,newton$$

$$6.675 \times {10^{ - 8}}\,newton$$

## Questions 46 of 50

Question:Two particles of equal mass go round a circle of radius R under the action of their mutual gravitational attraction. The speed of each particle is

$$v = \frac{1}{{2R}}\sqrt {\frac{1}{{Gm}}}$$

$$v = \sqrt {\frac{{Gm}}{{2R}}}$$

$$v = \frac{1}{2}\sqrt {\frac{{Gm}}{R}}$$

$$v = \sqrt {\frac{{4Gm}}{R}}$$

## Questions 47 of 50

Question:The earth (mass $$= 6 \times {10^{24}}\,kg)$$) revolves round the sun with angular velocity $$2 \times {10^{ - 7}}\,rad/s$$ in a circular orbit of radius $$1.5 \times {10^8}\,km$$. The force exerted by the sun on the earth in newtons, is

$$18 \times {10^{25}}$$

Zero

$$27 \times {10^{39}}$$

$$36 \times {10^{21}}$$

## Questions 48 of 50

Question:Two identical solid copper spheres of radius R placed in contact with each other. The gravitational attracton between them is proportional to

R$$^2$$

R$$^{ - 2}$$

R$$^{\rm{4}}$$

R$$^{--{\rm{4}}}$$

## Questions 49 of 50

Question:Imagine a light planet revolving around a very massive star in a circular orbit of radius R with a period of revolution T. If the gravitational forced of attraction between the planet and the star is proportional to $${R^{ - 5/2}}$$, then:

$${{\rm{T}}^{\rm{2}}}$$ is proportional to $${R^3}$$

$${{\rm{T}}^{\rm{2}}}$$ is proportional to $${R^{7/2}}$$

$${{\rm{T}}^{\rm{2}}}$$ is proportional to $${R^{3/2}}$$

$${{\rm{T}}^{\rm{2}}}$$ is proportional to $${R^3}$$

## Questions 50 of 50

Question:If g is the acceleration due to gravity on the earth's surface, the gain in the potential energy of an object of mass m raised from the surface of the earth to a height equal to the radius R of the earth, is

$$\frac{1}{2}$$mgR
$$\frac{1}{4}$$mgR