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%
The distance between centre of the earth and moon is 384000 km. If the mass of the earth is and . The speed of the moon is nearly -
1. 1 km/sec
2. 4 km/sec
3. 8 km/sec
4. 11.2 km/sec
A body is projected vertically upwards from the surface of a planet of radius \(R\) with a velocity equal to half the escape velocity for that planet. The maximum height attained by the body is:
1. \(\frac{R}{3}\)
2. \(\frac{R}{2}\)
3. \(\frac{R}{4}\)
4. \(\frac{R}{5}\)
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 \(1.02~\text{R}\). The percentage difference in the time periods of the two satellites is:
1. | \(0.7\) | 2. | \(1.0\) |
3. | \(1.5\) | 4. | \(3\) |
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
The kinetic energy needed to project a body of mass m from the earth surface (radius R) to infinity is -
1. mgR/2
2. 2 mgR
3. mgR
4. mgR/4
A satellite is to revolve round the earth in a circle of radius 8000 km. The speed at which this satellite be projected into an orbit, will be
1.
2. 16 km/s
3. 7.15 km/s
4. 8 km/s
If the mass of a body is M on the earth surface, then the mass of the same body on the moon surface is:
1. M/6
2. Zero
3. M
4. None of these