A thin rod of length L is bent to form a semicircle. The mass of the rod is M. The gravitational potential at the centre of the circle is :
1.
2.
3.
4.
The centripetal force acting on a satellite orbiting round the earth and the gravitational
force of earth acting on the satellite both equal F. The net force on the satellite is
1. Zero
2. F
3.
4. 2 F
An astronaut orbiting the earth in a circular orbit 120 km above the surface of earth, gently drops a spoon out of space-ship. The spoon will
1. Fall vertically down to the earth
3. Move towards the moon
4. Will move along with space-ship
4. Will move in an irregular way then fall down
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 force of attraction between planet and star is proportional to , then is proportional to
(1)
(2)
(3)
(4)
Two bodies of masses and are initially at rest at infinite distance apart. They are then allowed to move towards each other under mutual gravitational attraction. Their relative velocity of approach at a separation distance r between them is
(1)
(2)
(3)
(4)
The period of the moon’s rotation around the earth is nearly 29 days. If the moon’s mass were 2 fold, its present value and all other things remained unchanged, the period of the moon’s rotation would be nearly:
(1)
(2)
(3)
(4)29 days
The distance of a planet from the sun is \(5\) times the distance between the earth and the sun. The time period of the planet is:
1. | \(5^{3/2}\) years | 2. | \(5^{2/3}\) years |
3. | \(5^{1/3}\) years | 4. | \(5^{1/2}\) years |
In an elliptical orbit under gravitational force, in general
(1) Tangential velocity is constant
(2) Angular velocity is constant
(3) Radial velocity is constant
(4) Areal velocity is constant
Earth is revolving around the sun, if the distance of the Earth from the Sun is reduced to 1/4th of the present distance then the present year length reduced to -
(1)
(2)
(3)
(4)
The diagram showing the variation of gravitational potential of earth with distance r from the centre of earth is -
In planetary motion the areal velocity of position vector of a planet depends on angular velocity and the distance of the planet from Sun (r). If so the correct relation for areal velocity is -
(1)
(2)
(3)
(4)
By which curve will the variation of gravitational potential of a hollow sphere of radius R with distance be depicted
Which of the following graphs represents the motion of a planet moving about the sun ?
A shell of mass M and radius R has a point mass m placed at a distance r from its centre. The gravitational potential energy U (r) vs r will be
The diameters of two planets are in the ratio 4 : 1 and their mean densities in the ratio 1 : 2. The acceleration due to gravity on the planets will be in the ratio of:
1. 1 : 2
2. 2 : 3
3. 2 : 1
4. 4 : 1
At what altitude in metre will the acceleration due to gravity be 25% of that at the earth's surface (Radius of earth = R metre)
(1)
(2) R
(3)
(4)
At the surface of a certain planet, acceleration due to gravity is one-quarter of that on earth. If a brass ball is transported to this planet, then which one of the following statements is not correct?
1. | The mass of the brass ball on this planet is a quarter of its mass as measured on earth |
2. | The weight of the brass ball on this planet is a quarter of the weight as measured on earth |
3. | The brass ball has the same mass on the other planet as on earth |
4. | The brass ball has the same volume on the other planet as on earth |
Weight of 1 kg becomes 1/6 kg on moon. If radius of moon is , then the mass of moon will be -
(a) (b)
(c) (d)
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
(a) 10 hr (b)
(c) 6 hr (d)
A body of mass m kg starts falling from a point 2R above the Earth’s surface. Its kinetic energy when it has fallen to a point ‘R’ above the Earth’s surface, is:
[R - Radius of Earth, M - Mass of Earth, G - Gravitational Constant] -
1.
2.
3.
4.
Let g be the acceleration due to gravity at earth's surface and K be the rotational kinetic energy of the earth. Suppose the earth's radius decreases by 2% keeping all other quantities same, then
(1) g decreases by 2% and K decreases by 4%
(2) g decreases by 4% and K increases by 2%
(3) g increases by 4% and K increases by 4%
(4) g decreases by 4% and K increases by 4%
A satellite is launched into a circular orbit of radius R around the Earth while a second satellite is launched into an orbit of radius 1.02R. The percentage difference in the time periods of the two satellites is:
1. | 0.7 | 2. | 1.0 |
3. | 1.5 | 4. | 3 |
If the radius of the earth shrinks by 1.5% (mass remaining same), then the value of acceleration due to gravity changes -
(a) 1% (b) 2%
(c) 3% (d) 4%
Distance of geostationary satellite from the center of the Earth in terms of is-
(1)
(2)
(3)
(4)
Energy required to move a body of mass m from an orbit of radius 2R to 3R is
(1)
(2)
(3)
(4)
If the radius of the earth contracts by 2% and its mass remains the same, then weight of the body at the earth surface :
(1) Will decrease
(2) Will increase
(3) Will remain the same
(4) None of these
Radius of orbit of satellite of earth is R. Its kinetic energy is proportional to -
1.
2.
3. R
4.
Two satellite A and B, ratio of masses 3 : 1 are in circular orbits of radii r and 4r. Then ratio of total mechanical energy of A to B is
(1) 1 : 3
(2) 3 : 1
(3) 3 : 4
(4) 12 : 1
Potential energy of a satellite having mass ‘\(m\) and rotating at a height of \(6.4\times10^{6}~\text{m}\) from the earth surface is:
1. | \(-0.5~mgR_e\) |
2. | \(-mgR_e\) |
3. | \(-2~mgR_e\) |
4. | \(4~mgR_e\) |
A satellite moves round the earth in a circular orbit of radius R making one revolution per day. A second satellite moving in a circular orbit, moves round the earth once in 8 days. The radius of the orbit of the second satellite is -
(1) 8 R
(2) 4R
(3) 2R
(4) R
A satellite moves in a circle around the earth. The radius of this circle is equal to one half of the radius of the moon’s orbit. The satellite completes one revolution in
(1) lunar month
(2) lunar month
(3) lunar month
(4) lunar month
If the acceleration due to gravity at a height 1 km above the earth is similar to a depth d below the surface of the earth, then:
1. d=0.5 km
2. d=1 km
3. d=1.5 km
4. d=2 km
Starting from the centre of the earth having radius R, the variation of g (acceleration due to gravity) is shown by:
(a)
(b)
(c)
(d)
A satellite of mass m is orbiting the earth [of radius R] at a height h from its surface. The total energy of the satellite in terms of , the value of acceleration due to gravity at the earth's surface is:
1. \(\frac{mg_0R^2}{2(R+h)}\)
2. \(-\frac{mg_0R^2}{2(R+h)}\)
3. \(\frac{2mg_0R^2}{R+h}\)
4. \(-\frac{2mg_0R^2}{R+h}\)
At what height from the surface of earth the gravitation potential and the value of g are and respectively? (Take, the radius of earth as 6400 km.)
(a) 1600 km (b) 1400 km
(c) 2000 km (d) 2600 km
A remote sensing satellite of the earth revolves in a circular orbit at a height of 0.25 x 106 m above the surface of the earth. If the earth’s radius is 6.38x106 m and g=9.8ms-1, then the orbital speed of the satellite is:
1. 7.76 kms-1
2. 8.56 kms-1
3. 9.13 kms-1
4. 6.67 kms-1
A satellite S is moving in an elliptical orbit around the earth. The mass of the satellite is very small as compared to the mass of the earth. Then,
(1) the angular momentum of S about the centre of the earth changes in direction, but its magnitude remains constant
(2) the total mechanical energy of S varies periodically with time
(3) the linear momentum of S remains constant in magnitude
(4) the acceleration of S is always directed towards the centre of the earth
Infinite number of bodies, each of mass 2 kg are situated on x-axis at distance 1m, 2m, 4m, 8m, respectively from the origin. The resulting gravitational potential due to this system at the origin will be
(a)-G
(b)-8/3G
(c)-4/3G
(d)-4G
A geostationary satellite is orbiting the earth at a height of 5R above the surface of the earth, R being the radius of the earth. The time period of another satellite in hours at a height of 2R from the surface of the earth is
1. 5
2.10
3. 6
4. 6/
A planet moving along an elliptical orbit is closest to the sun at a distance and farthest away at a distance of . If are the linear velocities at these points respectively, then the ratio is:
(1)
(2)
(3)
(4)
A particle of mass M is situated at the centre of a spherical shell of mass M and radius a.The gravitational potential at a point situated at a/2 distance from the centre will be
1. 2.
3. 4.
The dependence of acceleration due to gravity g on the distance r from the centre of the earth assumed to be a sphere of radius R of uniform density is as shown in the figure below -
(1) (2)
(3) (4)
The correct figure is
(a) (1) (b) (3)
(c) (2) (d) (4)
The figure shows elliptical orbit of a planet m about the sun S. The shaded area SCD is twice the shaded area SAB. If is the time for planet to move from C to D and is the time to move from A to B, then
(1)
(2)
(3)
(4)
A body of mass m rises to height h = R/5 from the earth's surface, where R is earth's radius. If g is acceleration due to gravity at earth's surface, the increase in potential energy is -
1. mgh
2.
3.
4.
Kepler's third law states that the square of the period of revolution (\(T\)) of a planet around the sun, is proportional to the third power of average distance \(r\) between the sun and planet i.e. \(T^2 = Kr^3\), here \(K\) is constant. If the masses of the sun and planet are \(M\) and \(m\) respectively, then as per Newton's law of gravitation, the force of attraction between them is \(F = \frac{GMm}{r^2},\) here \(G\) is the gravitational constant. The relation between \(G\) and \(K\) is described as:
1. \(GK = 4\pi^2\)
2. \(GMK = 4\pi^2\)
3. \(K =G\)
4. \(K = \frac{1}{G}\)