A straight rod of length L extends from x = a to x = L + a. The gravitational force it exerts on a point mass m at x = 0, if the mass per unit length of the rod is A + Bx2, is given by

\(Gm\left[ {A\left( {\frac{1}{a} - \frac{1}{{a + L}}} \right) - BL} \right]\)

\(Gm\left[ {A\left( {\frac{1}{{a + L}} - \frac{1}{a}} \right) - BL} \right]\)

\(Gm\left[ {A\left( {\frac{1}{{a + L}} - \frac{1}{a}} \right) + BL} \right]\)

\(Gm\left[ {A\left( {\frac{1}{a} - \frac{1}{{a + L}}} \right) + BL} \right]\)

\(Gm\left[ {A\left( {\frac{1}{a} - \frac{1}{{a + L}}} \right) - BL} \right]\)

Direction: Given question consists of two statements, one labeled as the 'Assertion (A)' and the other as 'Reason (R)'. You are to examine these two statements carefully and select the answers to these items using the codes given below.Assertion (A): A geostationary orbit is the same as a geosynchronous orbit.Reason (R): A geostationary orbit does not necessarily lie in the equatorial plane.

Both A and R are individually true and R is the correct explanation of A

Both A and R are individually true but R is NOT the correct explanation of A

Direction: Given question consists of two statements, one labeled as the 'Assertion (A)' and the other as 'Reason (R)'. You are to examine these two statements carefully and select the answers to these items using the codes given below.Assertion (A): A passive satellite only reflects back signals.Reason (R): A communication satellite is a repeater between many transmitting stations and many receiving stations.

Both A and R are individually true and R is the correct explanation of A

Both A and R are individually true but R is NOT the correct explanation of A

Earth rotates about its axis with angular velocity ω. An object weighed by a spring balance gives the same reading at the equator and at a height h above the poles (h

\(\frac{{2{\omega ^2}{R^2}}}{g}\)

\(\frac{{{\omega ^2}{R^2}}}{g}\)

\(\frac{{{\omega ^2}{R^2}}}{{2g}}\)

\(\frac{{2{\omega ^2}{R^2}}}{g}\)

\(\frac{{\sqrt {Rg} }}{\omega }\)

Expression for time in terms of G (universal gravitational constant), h (Planck constant) and c (speed of light) is proportional to:

\(\sqrt {\frac{{{\rm{Gh}}}}{{{{\rm{c}}^3}}}} \)

\(\sqrt {\frac{{{\rm{h}}{{\rm{c}}^5}}}{{\rm{G}}}} \)

\(\sqrt {\frac{{{{\rm{c}}^3}}}{{{\rm{Gh}}}}} \)

\(\sqrt {\frac{{{\rm{Gh}}}}{{{{\rm{c}}^5}}}}\)

\(\sqrt {\frac{{{\rm{Gh}}}}{{{{\rm{c}}^3}}}} \)

Light Interferometer Gravitational wave Observatory

Laser Interferometer Gravitational wave Observatory

Light Interferometer Gravitational wave Observatory

Light Induced Gravity Observatory

Mass of the earth is M and its radius is R. An object of mass m is placed on the surface of earth. Find the work done in lifting the object through a height \(\frac{R}{2}\) above the surface of earth.

\(\frac{{2{\rm{\;}}GMm}}{{3R}}\)

As we move from the equator towards the N-pole, while remaining on the surface of earth the value of g

increases and decreases periodically

In a car race on straight road, car A takes a time ‘t’ less than car B at the finish and passes finishing point with a speed ‘v’ more than that of car B. Both the cars start from rest and travel with constant acceleration \({{\rm{a}}_1}\) and \({{\rm{a}}_2}\) respectively. Then ‘v’ is equal to:

\(\frac{{2{a_1}{a_2}}}{{{a_1} + {a_2}}}t\)

Kepler's II law is a consequence of-

Conservation of angular momentum

A satellite moving in a circular orbit around Earth. If gravitational pull suddenly disappears, then it

Falls down with increasing speed

Continues to move in same path in same speed

Moves same speed tangential to original orbit

Falls down with increasing speed

Comes to rest and stays at the same height

‘Black hole’ is a

star which has collapsed into itself and has zero acceleration due to gravity on its surface

huge black star which has zero acceleration due to gravity on its surface

star which has moderate acceleration due to gravity on its surface

star which has collapsed into itself and has large acceleration due to gravity on its surface

star which has collapsed into itself and has zero acceleration due to gravity on its surface

A geostationary orbit is chosen for communication satellites because:

This orbit provides earth's coverage of more than 50% using a single satellite

It is stationary at one point in space

With respect to a spot on earth it looks stationary

This orbit provides earth's coverage of more than 50% using a single satellite

The length of 4700 km is convenient for launching

A ball is thrown upward with an initial velocity V0 from the surface of the earth. The motion of the ball is affected by a drag force equal to mγv2 (where m is mass of the ball, v is its instantaneous velocity and γ is a constant). Time taken by the ball to rise to its zenith is:

\(\frac{1}{{\sqrt {\gamma {\rm{g}}} }}{\rm{si}}{{\rm{n}}^{ - 1}}\left( {\sqrt {\frac{\gamma }{g}} {{\rm{V}}_0}} \right)\)

\(\frac{1}{{\sqrt {\gamma {\rm{g}}} }}{\rm{ta}}{{\rm{n}}^{ - 1}}\left( {\sqrt {\frac{\gamma }{{\rm{g}}}} {{\rm{V}}_0}} \right)\)

\(\frac{1}{{\sqrt {\gamma {\rm{g}}} }}{\rm{si}}{{\rm{n}}^{ - 1}}\left( {\sqrt {\frac{\gamma }{g}} {{\rm{V}}_0}} \right)\)

\(\frac{1}{{\sqrt {\gamma {\rm{g}}} }}{\rm{ln}}\left( {1 + \sqrt {\frac{\gamma }{{\rm{g}}}} {{\rm{V}}_0}} \right)\)

\(\frac{1}{{\sqrt {2\gamma {\rm{g}}} }}{\rm{ta}}{{\rm{n}}^{ - 1}}\left( {\sqrt {\frac{{2\gamma }}{{\rm{g}}}} {{\rm{V}}_0}} \right)\)

Mass of uniform circular ring is M and its radius is R. Find the maximum intensity of gravitation field on the axis of the ring

\(\frac{2}{{3\sqrt 3 }}\frac{{GM}}{{{R^2}}}\)

\(\frac{3}{{2\sqrt 2 }}\frac{{GM}}{{{R^2}}}\)

72 + Mcqs in Gravitation in UPSEE Page 1 McqOptions

1.	In a vacuum, a five-rupee coin, a feather of a sparrow bird and a mango are dropped simultaneously from the same height. The time taken by them to reach the bottom is t1, t2 and t3 respectively. In this situation, we will observe that
A.	t1> t2 >t3
B.	t1> t3 >t2
C.	t3> t1 >t2
D.	t1= t2 =t3
Answer» E.

Discussion

2.	If the acceleration due to gravity is 12.6 m/s2 on a planet of 1/7th the mass of earth, then what must be its radius as compared to 'R', the radius of the earth?
A.	R/2
B.	R/3
C.	3R/2
D.	2R/3
Answer» C. 3R/2

Discussion

3.	A satellite moves around the earth in a circular orbit of radius R centered at the earth. A second satellite moves in an elliptical orbit of major axis 8R, with the earth at one of the foci. If the former takes 1 day to complete a revolution, later would take
A.	21.6 days
B.	3 hours
C.	1.1 hours
D.	8 days
Answer» E.

Discussion

4.	Every object in the universe attracts every other object. This force is called _________.
A.	Gravitation
B.	Gravity
C.	Attraction
D.	Celestial force
Answer» B. Gravity

Discussion

5.	Geostationary orbit is at a height of approx ___________.
A.	6 km
B.	1,000 km
C.	3,600 km
D.	36,000 km
Answer» E.

Discussion

6.	If a body of mass 'm' moves in a circular orbit of radius 'a' about another body of mass 'M', where M >> m, then total energy of the system is ____________.
A.	E = -GMm/a
B.	E = -GMm/(2a)
C.	E = -GMm/(2a2)
D.	E = -GMm/a2
Answer» C. E = -GMm/(2a2)

Discussion

7.	A particle starts from origin O from rest and moves with a uniform acceleration along the positive x-axis. Identify all figures that correctly represent the motion qualitatively. (a = acceleration, v = velocity, x = displacement, t = time).A.B. C. D.
A.	A
B.	A, B, C
C.	A, B, D
D.	B, C
Answer» D. B, C

Discussion

8.	In a simple pendulum experiment for determination of acceleration due to gravity (g), time taken for 20 oscillations is measured by using a watch of 1 second least count. The mean value of time taken comes out to be 30 s. The length of pendulum is measured by using a meter scale of least count 1 mm and the value obtained is 55.0 cm. The percentage error in the determination of g is close to:
A.	0.7%
B.	0.2%
C.	3.5%
D.	6.8%
Answer» E.

Discussion

9.	_____ argued that all planets are in the Sun's orbit, not Earth's, contrary to the belief of the time.
A.	Johann Wolfgang Dobreiner
B.	Gregor Mendel
C.	Galileo Galilei
D.	Isaac Newton
Answer» D. Isaac Newton

Discussion

10.	In 2009, TerreStar-1 was launched for better communication to North America. From which country was it launched?A. FranceB. AmericaC. ChinaD. Russia
A.	A
B.	B
C.	D
D.	C
Answer» B. B

Discussion

11.	NASA released a picture of crashed Vikram lander on 3, December 2019. Which satellite did NASA use to find Vikram?
A.	Skylab
B.	Lunar Reconnaissance Orbiter
C.	Explorer 1
D.	Juno
Answer» C. Explorer 1

Discussion

12.	A straight rod of length L extends from x = a to x = L + a. The gravitational force it exerts on a point mass m at x = 0, if the mass per unit length of the rod is A + Bx2, is given by
A.	\(Gm\left[ {A\left( {\frac{1}{{a + L}} - \frac{1}{a}} \right) - BL} \right]\)
B.	\(Gm\left[ {A\left( {\frac{1}{{a + L}} - \frac{1}{a}} \right) + BL} \right]\)
C.	\(Gm\left[ {A\left( {\frac{1}{a} - \frac{1}{{a + L}}} \right) + BL} \right]\)
D.	\(Gm\left[ {A\left( {\frac{1}{a} - \frac{1}{{a + L}}} \right) - BL} \right]\)
Answer» D. \(Gm\left[ {A\left( {\frac{1}{a} - \frac{1}{{a + L}}} \right) - BL} \right]\)

Discussion

13.	Once a satellite has been launched into orbit, the only force governing its motion is the force of ______ .
A.	gravity
B.	elasticity
C.	friction
D.	fuel driven
Answer» B. elasticity

Discussion

14.	Imagine that there exists a planet that has half the radius of the earth and half its mass. Then, the acceleration due to gravity on the surface of that planet in relation to the acceleration due to gravity g on the surface of the earth is
A.	g' = g/4
B.	g' = 2g
C.	g' = g
D.	g' = g/2
Answer» C. g' = g

Discussion

15.	Direction: Given question consists of two statements, one labeled as the 'Assertion (A)' and the other as 'Reason (R)'. You are to examine these two statements carefully and select the answers to these items using the codes given below.Assertion (A): A geostationary orbit is the same as a geosynchronous orbit.Reason (R): A geostationary orbit does not necessarily lie in the equatorial plane.
A.	Both A and R are individually true and R is the correct explanation of A
B.	Both A and R are individually true but R is NOT the correct explanation of A
C.	A is true but R is false
D.	A is false but R is true
Answer» D. A is false but R is true

Discussion

16.	A satellite goes along an elliptical path around the earth. The time period of the satellite is proportional to-
A.	r1/2
B.	r
C.	r3/2
D.	r2
Answer» D. r2

Discussion

17.	Let 'K' be the area swept by the line joining the earth and the sun during Feb 2012. The area swept by the same line during the first week of that mouth is
A.	7K/30
B.	K
C.	K/4
D.	7K/29
Answer» E.

Discussion

18.	If 'r' is the radius of circular orbit then the orbital period of a satellite is directly proportional to:
A.	\(r^{\frac 3 2}\)
B.	\(r^{\frac 1 3}\)
C.	\(r^{\frac 1 2}\)
D.	\(r^{\frac 2 3}\)
Answer» B. \(r^{\frac 1 3}\)

Discussion

19.	Direction: Given question consists of two statements, one labeled as the 'Assertion (A)' and the other as 'Reason (R)'. You are to examine these two statements carefully and select the answers to these items using the codes given below.Assertion (A): A passive satellite only reflects back signals.Reason (R): A communication satellite is a repeater between many transmitting stations and many receiving stations.
A.	Both A and R are individually true and R is the correct explanation of A
B.	Both A and R are individually true but R is NOT the correct explanation of A
C.	A is true but R is false
D.	A is false but R is true
Answer» C. A is true but R is false

Discussion

20.	Earth rotates about its axis with angular velocity ω. An object weighed by a spring balance gives the same reading at the equator and at a height h above the poles (h << R) By assuming the acceleration due to gravity to be same at the equator and at poles without rotating earth, then the value of h is
A.	\(\frac{{{\omega ^2}{R^2}}}{g}\)
B.	\(\frac{{{\omega ^2}{R^2}}}{{2g}}\)
C.	\(\frac{{2{\omega ^2}{R^2}}}{g}\)
D.	\(\frac{{\sqrt {Rg} }}{\omega }\)
Answer» C. \(\frac{{2{\omega ^2}{R^2}}}{g}\)

Discussion

21.	At a height equal to earth's radius, above the earth surface, the acceleration due to gravity is-
A.	g
B.	g/2
C.	g/4
D.	g/8
Answer» D. g/8

Discussion

22.	If g on the surface of the earth is \(10m/s^2\), its value at a height of 6400 km is (Radius of the earth = 6400 km)
A.	\(5 \ ms^{-2}\)
B.	\(20 \ ms^{-2}\)
C.	\(2.5 \ ms^{-2}\)
D.	\(10 \ ms^{-2}\)
Answer» D. \(10 \ ms^{-2}\)

Discussion

23.	If the earth is 1/4 of its present distance from the sun, then the duration of the year would be
A.	1/2 year
B.	1/4 year
C.	1/8 year
D.	1/16
Answer» D. 1/16

Discussion

24.	A test particle is moving in circular orbit in the gravitational field produced by a mass density \(\rho \left( r \right) = \frac{K}{{{r^2}}}\). Identify the correct relation between the radius R of the particle's orbit and its period T:
A.	T/R is a constant
B.	T2/R3 is a constant
C.	T/R2 is a constant
D.	TR is a constant
Answer» B. T2/R3 is a constant

Discussion

25.	A satellite revolves round a planet at 100 km circular polar orbit with a period of 126 minutes. What will be the orbital period if the orbit is raised to 200 km?
A.	50 minutes
B.	126 minutes
C.	200 minutes
D.	357 minutes
Answer» E.

Discussion

26.	Expression for time in terms of G (universal gravitational constant), h (Planck constant) and c (speed of light) is proportional to:
A.	\(\sqrt {\frac{{{\rm{h}}{{\rm{c}}^5}}}{{\rm{G}}}} \)
B.	\(\sqrt {\frac{{{{\rm{c}}^3}}}{{{\rm{Gh}}}}} \)
C.	\(\sqrt {\frac{{{\rm{Gh}}}}{{{{\rm{c}}^5}}}}\)
D.	\(\sqrt {\frac{{{\rm{Gh}}}}{{{{\rm{c}}^3}}}} \)
Answer» D. \(\sqrt {\frac{{{\rm{Gh}}}}{{{{\rm{c}}^3}}}} \)

Discussion

27.	A women whose mass is 60 kg on the earth surface is in an spacecraft at an altitude of two times the earth radius. Her mass there is
A.	6.7 kg
B.	15 kg
C.	20 kg
D.	60 kg
Answer» E.

Discussion

28.	If radius of the earth were to shrink by 1%, its mass remains the same, g would decrease by nearly
A.	1%
B.	2%
C.	3%
D.	4%
Answer» C. 3%

Discussion

29.	LIGO stands for
A.	Laser Interferometer Gravitational wave Observatory
B.	Light Interferometer Gravitational wave Observatory
C.	Light Induced Gravity Observatory
D.	Laser Induced Gaseous Optics
Answer» B. Light Interferometer Gravitational wave Observatory

Discussion

30.	If three particles, each of mass M are placed at the three corners of an equilateral triangle of side a, the force exerted by this system on another particle of mass M placed at the midpoint of a side is
A.	4GM2 / 5a2
B.	4GM2 / 3a2
C.	2GM2 / 3a2
D.	2GM2 / 5a2
Answer» C. 2GM2 / 3a2

Discussion

31.	Mass of the earth is M and its radius is R. An object of mass m is placed on the surface of earth. Find the work done in lifting the object through a height \(\frac{R}{2}\) above the surface of earth.
A.	\(\frac{{GMm}}{{2R}}\)
B.	\(\frac{{GMm}}{{3R}}\)
C.	\(\frac{{2{\rm{\;}}GMm}}{{3R}}\)
D.	\(\frac{{GMm}}{{4R}}\)
Answer» C. \(\frac{{2{\rm{\;}}GMm}}{{3R}}\)

Discussion

32.	As we move from the equator towards the N-pole, while remaining on the surface of earth the value of g
A.	increases and decreases periodically
B.	increases
C.	does not change
D.	decreases
Answer» C. does not change

Discussion

33.	A spaceship orbits around a planet at a height of 20 km from its surface. Assuming that only gravitational field of the planet acts on the spaceship, what will be the number of complete revolutions made by the spaceship in 24 hours around the planet?[Given: Mass of planet = 8 × 1022 kgRadius of planet = 2 × 106 mGravitational constant, G = 6.67 × 10-11 Nm2/kg2]
A.	9
B.	17
C.	13
D.	11
Answer» E.

Discussion

34.	In a car race on straight road, car A takes a time ‘t’ less than car B at the finish and passes finishing point with a speed ‘v’ more than that of car B. Both the cars start from rest and travel with constant acceleration \({{\rm{a}}_1}\) and \({{\rm{a}}_2}\) respectively. Then ‘v’ is equal to:
A.	\(\frac{{2{a_1}{a_2}}}{{{a_1} + {a_2}}}t\)
B.	\(\sqrt {2{a_1}{a_2}} t\)
C.	\(\sqrt {{a_1}{a_2}} t\)
D.	\(\frac{{{a_1} + {a_2}}}{2}t\)
Answer» D. \(\frac{{{a_1} + {a_2}}}{2}t\)

Discussion

35.	Kepler's II law is a consequence of-
A.	Conservation of energy
B.	Conservation of liner momentum
C.	Conservation of angular momentum
D.	None of these
Answer» D. None of these

Discussion

36.	A satellite moving in a circular orbit around Earth. If gravitational pull suddenly disappears, then it
A.	Continues to move in same path in same speed
B.	Moves same speed tangential to original orbit
C.	Falls down with increasing speed
D.	Comes to rest and stays at the same height
Answer» C. Falls down with increasing speed

Discussion

37.	Geo-stationary satellites are placed in equatorial orbits at the height approximately
A.	1000 km
B.	15000 km
C.	25000 km
D.	36000 km
Answer» E.

Discussion

38.	Find the magnitude of the gravitational force between two protons separated by a distance of 1 Å. It is given that mp = 5/3 × 10-27 kg.G = 20/3 × 10-11 Nm2kg-2
A.	\(\dfrac{10^{-42}}{27}N\)
B.	\(\dfrac{10^{-42}}{54}N\)
C.	\(\dfrac{10^{-42}}{36}N\)
D.	\(\dfrac{10^{-41}}{27}N\)
Answer» C. \(\dfrac{10^{-42}}{36}N\)

Discussion

39.	If the universal gravitational constant were decreasing with time, then satellite in orbit would still maintain its:
A.	Orbital radius
B.	Angular momentum
C.	Tangential speed
D.	Period of revolution
Answer» C. Tangential speed

Discussion

40.	‘Black hole’ is a
A.	huge black star which has zero acceleration due to gravity on its surface
B.	star which has moderate acceleration due to gravity on its surface
C.	star which has collapsed into itself and has large acceleration due to gravity on its surface
D.	star which has collapsed into itself and has zero acceleration due to gravity on its surface
Answer» D. star which has collapsed into itself and has zero acceleration due to gravity on its surface

Discussion

41.	A geostationary orbit is chosen for communication satellites because:
A.	It is stationary at one point in space
B.	With respect to a spot on earth it looks stationary
C.	This orbit provides earth's coverage of more than 50% using a single satellite
D.	The length of 4700 km is convenient for launching
Answer» C. This orbit provides earth's coverage of more than 50% using a single satellite

Discussion

42.	A man weighs 'W' on the surface of earth and his weight at a height '2R' from surface of earth is (R is the Radius of earth).
A.	\(\frac{w}{9}\)
B.	\(\frac{w}{6}\)
C.	\(W\)
D.	\(\frac{w}{3}\)
Answer» B. \(\frac{w}{6}\)

Discussion

43.	A ball is thrown upward with an initial velocity V0 from the surface of the earth. The motion of the ball is affected by a drag force equal to mγv2 (where m is mass of the ball, v is its instantaneous velocity and γ is a constant). Time taken by the ball to rise to its zenith is:
A.	\(\frac{1}{{\sqrt {\gamma {\rm{g}}} }}{\rm{ta}}{{\rm{n}}^{ - 1}}\left( {\sqrt {\frac{\gamma }{{\rm{g}}}} {{\rm{V}}_0}} \right)\)
B.	\(\frac{1}{{\sqrt {\gamma {\rm{g}}} }}{\rm{si}}{{\rm{n}}^{ - 1}}\left( {\sqrt {\frac{\gamma }{g}} {{\rm{V}}_0}} \right)\)
C.	\(\frac{1}{{\sqrt {\gamma {\rm{g}}} }}{\rm{ln}}\left( {1 + \sqrt {\frac{\gamma }{{\rm{g}}}} {{\rm{V}}_0}} \right)\)
D.	\(\frac{1}{{\sqrt {2\gamma {\rm{g}}} }}{\rm{ta}}{{\rm{n}}^{ - 1}}\left( {\sqrt {\frac{{2\gamma }}{{\rm{g}}}} {{\rm{V}}_0}} \right)\)
Answer» B. \(\frac{1}{{\sqrt {\gamma {\rm{g}}} }}{\rm{si}}{{\rm{n}}^{ - 1}}\left( {\sqrt {\frac{\gamma }{g}} {{\rm{V}}_0}} \right)\)

Discussion

44.	A satellite moving in a circular orbit around earth has a total (kinetic + potential) energy Eo. Its potential energy will be ____
A.	2Eo
B.	Eo
C.	Eo/4
D.	Eo/2
Answer» B. Eo

Discussion

45.	A planet has a mass M1 and radius R1. The value of acceleration due to gravity on its surface is g1. There is another planet 2, whose mass and radius both are two times that of the first planet. Which one of the following is the acceleration due to gravity on the surface of planet 2?
A.	g1
B.	2g1
C.	g1/2
D.	g1/4
Answer» D. g1/4

Discussion

46.	Mass of uniform circular ring is M and its radius is R. Find the maximum intensity of gravitation field on the axis of the ring
A.	\(\frac{2}{{3\sqrt 3 }}\frac{{GM}}{{{R^2}}}\)
B.	\(\frac{{GM}}{{{R^2}}}\)
C.	\(\frac{{2GM}}{{{R^2}}}\)
D.	\(\frac{3}{{2\sqrt 2 }}\frac{{GM}}{{{R^2}}}\)
Answer» B. \(\frac{{GM}}{{{R^2}}}\)

Discussion

47.	If earth shrinks by one third of its present radius, the acceleration due to gravity will be-
A.	\(\frac{2}{3}\)g
B.	\(\frac{3}{2}\)g
C.	\(\frac{4}{9}\)g
D.	\(\frac{9}{4}\)g
Answer» B. \(\frac{3}{2}\)g

Discussion

48.	If earth has a mass nine times and radius twice that of the planet mars, calculate the maximum velocity required by a rocket to escape from the gravitational field of mars. Take escape velocity on the earth's surface to be 11.2 km/s.
A.	5.279 km/s
B.	23.75 km/s
C.	9144 km/s
D.	3.865 km/s
Answer» B. 23.75 km/s

Discussion

49.	Pick out the non-luminous object from the options below.
A.	Sun
B.	Moon
C.	Stars
D.	Electric Bulb
Answer» C. Stars

Discussion

50.	A planet moves around the sun in elliptical orbit. When earth is closest from the sun, it is at a distance γ having a speed v. When it is at a distance 4γ from the sun its speed is :
A.	v/4
B.	4v
C.	2v
D.	v/2
Answer» B. 4v

Discussion

Explore topic-wise MCQs in UPSEE.

In a vacuum, a five-rupee coin, a feather of a sparrow bird and a mango are dropped simultaneously from the same height. The time taken by them to reach the bottom is t1, t2 and t3 respectively. In this situation, we will observe that

If the acceleration due to gravity is 12.6 m/s2 on a planet of 1/7th the mass of earth, then what must be its radius as compared to 'R', the radius of the earth?

A satellite moves around the earth in a circular orbit of radius R centered at the earth. A second satellite moves in an elliptical orbit of major axis 8R, with the earth at one of the foci. If the former takes 1 day to complete a revolution, later would take

Every object in the universe attracts every other object. This force is called _________.

Geostationary orbit is at a height of approx ___________.

If a body of mass 'm' moves in a circular orbit of radius 'a' about another body of mass 'M', where M >> m, then total energy of the system is ____________.

A particle starts from origin O from rest and moves with a uniform acceleration along the positive x-axis. Identify all figures that correctly represent the motion qualitatively. (a = acceleration, v = velocity, x = displacement, t = time).A.B. C. D.

_____ argued that all planets are in the Sun's orbit, not Earth's, contrary to the belief of the time.

In 2009, TerreStar-1 was launched for better communication to North America. From which country was it launched?A. FranceB. AmericaC. ChinaD. Russia

NASA released a picture of crashed Vikram lander on 3, December 2019. Which satellite did NASA use to find Vikram?

A straight rod of length L extends from x = a to x = L + a. The gravitational force it exerts on a point mass m at x = 0, if the mass per unit length of the rod is A + Bx2, is given by

Once a satellite has been launched into orbit, the only force governing its motion is the force of ______ .

Imagine that there exists a planet that has half the radius of the earth and half its mass. Then, the acceleration due to gravity on the surface of that planet in relation to the acceleration due to gravity g on the surface of the earth is

A satellite goes along an elliptical path around the earth. The time period of the satellite is proportional to-

Let 'K' be the area swept by the line joining the earth and the sun during Feb 2012. The area swept by the same line during the first week of that mouth is

If 'r' is the radius of circular orbit then the orbital period of a satellite is directly proportional to:

At a height equal to earth's radius, above the earth surface, the acceleration due to gravity is-

If g on the surface of the earth is \(10m/s^2\), its value at a height of 6400 km is (Radius of the earth = 6400 km)

If the earth is 1/4 of its present distance from the sun, then the duration of the year would be

A test particle is moving in circular orbit in the gravitational field produced by a mass density \(\rho \left( r \right) = \frac{K}{{{r^2}}}\). Identify the correct relation between the radius R of the particle's orbit and its period T:

A satellite revolves round a planet at 100 km circular polar orbit with a period of 126 minutes. What will be the orbital period if the orbit is raised to 200 km?

Expression for time in terms of G (universal gravitational constant), h (Planck constant) and c (speed of light) is proportional to:

A women whose mass is 60 kg on the earth surface is in an spacecraft at an altitude of two times the earth radius. Her mass there is

If radius of the earth were to shrink by 1%, its mass remains the same, g would decrease by nearly

LIGO stands for

If three particles, each of mass M are placed at the three corners of an equilateral triangle of side a, the force exerted by this system on another particle of mass M placed at the midpoint of a side is

Mass of the earth is M and its radius is R. An object of mass m is placed on the surface of earth. Find the work done in lifting the object through a height \(\frac{R}{2}\) above the surface of earth.

As we move from the equator towards the N-pole, while remaining on the surface of earth the value of g

Kepler's II law is a consequence of-

A satellite moving in a circular orbit around Earth. If gravitational pull suddenly disappears, then it

Geo-stationary satellites are placed in equatorial orbits at the height approximately

Find the magnitude of the gravitational force between two protons separated by a distance of 1 Å. It is given that mp = 5/3 × 10-27 kg.G = 20/3 × 10-11 Nm2kg-2

If the universal gravitational constant were decreasing with time, then satellite in orbit would still maintain its:

‘Black hole’ is a

A geostationary orbit is chosen for communication satellites because:

A man weighs 'W' on the surface of earth and his weight at a height '2R' from surface of earth is (R is the Radius of earth).

A ball is thrown upward with an initial velocity V0 from the surface of the earth. The motion of the ball is affected by a drag force equal to mγv2 (where m is mass of the ball, v is its instantaneous velocity and γ is a constant). Time taken by the ball to rise to its zenith is:

A satellite moving in a circular orbit around earth has a total (kinetic + potential) energy Eo. Its potential energy will be ____

A planet has a mass M1 and radius R1. The value of acceleration due to gravity on its surface is g1. There is another planet 2, whose mass and radius both are two times that of the first planet. Which one of the following is the acceleration due to gravity on the surface of planet 2?

Mass of uniform circular ring is M and its radius is R. Find the maximum intensity of gravitation field on the axis of the ring

If earth shrinks by one third of its present radius, the acceleration due to gravity will be-

If earth has a mass nine times and radius twice that of the planet mars, calculate the maximum velocity required by a rocket to escape from the gravitational field of mars. Take escape velocity on the earth's surface to be 11.2 km/s.

Pick out the non-­luminous object from the options below.

A planet moves around the sun in elliptical orbit. When earth is closest from the sun, it is at a distance γ having a speed v. When it is at a distance 4γ from the sun its speed is :

Pick out the non-luminous object from the options below.