A satellite is revolving round the earth. Its K.E is Ek. How much would it be made so that the satellite may escape out of the gravitational field of earth?
2Ek
3Ek
Ek/2
Infinite
The time period of an earth satellite in circular orbit is independent of :
both the mass and radius of the orbit
neither the mass of the satellite nor the radius of its orbit
the mass of the satellite
radius of its orbit
If the radius of the earth is made three times, keeping its mass constant, then the weight of a body on earth's surface will be as compared to its previous value :
3 times
9 times
A planet in a distant solar system is 10 times more massive than the earth and its radius is 10 times smaller. Given that the escape velocity from the earth is 11kms-1, the escape velocity from the surface of the planet would be :
110 kms-1
0.11 kms-1
1.1 kms-1
11 kms-1
An infinity number of point masses each equal to m are placed at x = 1, x = 2, x = 4, x = 8, ..... What is the total gravitational potential at x - 0?
-Gm
-2Gm
-4Gm
-8 Gm
Suppose the gravitational force varies inversely as the nth power of distance. Then the time period of a planet in circular orbit of radius R around the sun will be proportional to :
Rn
If the radius of the earth decreases by 10%, the mass remaining unchanged, what will happen to the acceleration due to gravity?
Decreases by 19%
Increases by 19%
Decreases by more than 19%
Increases by more than 19%
Two spherical bodies of mass M and 5M and radii R and 2R respectively are released in free space with initial separation between their centres equal to 12R. If they attract each other due to gravitational force only, then the distance covered by the smaller body just before collision is :
7.5 R
1.5 R
2.5 R
4.5 R
A satellite moves eastwards very near the surface of the earth in the equatorial plane of the earth with speed v0. Another satellite moves at the same height with the same speed in the equatorial plane but westwards. If R is the radius of the earth and ω be its angular speed about its own axis, then the difference in the two time period as observed on the earth will be approximately equal to :
The kinetic energy needed to project a body of mass m from the earth's surface (radius R) to infinity is :
mgR
2mgR