A planet is moving in an elliptical orbit around the sun. If T, U, E and L stands for its kinetic energy, gravitational potential energy, total energy and magnitude of angular momentum about the centre of force, which of the following is correct?
T is conserved
U is always positive
E is always negative
L is conserved but direction of vector L changes continuously
A second pendulum is mounted in a rocket. Its period of oscillation decreases when the rocket
Comes down with uniform acceleration
Moves round the earth in a geostationary orbit
Moves up with a uniform velocity
Moves up with uniform acceleration
The escape velocity of a sphere of mass m is given by (G = universal gravitational constant, Me = mass of earth and Re = radius of earth)
The acceleration due to gravity on the planet A is 9 times the acceleration due to gravity on planet B. A man jumps to a height of 2m on the surface of A. What is the height of jump by the same person on the planet B?
6 m
2/3 m
2/9 m
18 m
The mean radius of earth is R, its angular speed on its own axis is ω and the acceleration due to gravity at earth's surface is g. What will be the radius of the orbit of a geostationary satellite?
The satellite of mass m is orbiting around the earth in a circular orbit with a velocity v. What will be its total energy?
3/4 mv2
1/2 mv2
mv2
- (1/2)mv2
A body of mass m is placed on earth's surface. It is then taken from earth's surface to a height h = 3R, then the change in gravitational potential energy is
mgh/R
2/3 mgR
3/4 mgR
mgR/2
Two spheres of masses m and M are situated in air and the gravitational force between them is F. The space around the masses is now filled with a liquid of specific gravity 3. The gravitational force will now be
F/3
F/9
3F
F
A satellite A of mass m is at a distance r from the surface of the earth. Another satellite B of mass 2 m is at a distance of 2 r from the earth's surface. Their time periods are in the ratio of
1 : 2
1 : 6
1 : 16
1 : 2√2
The period of revolution of planet A around the sun is 8 times that of B. The distance of A from the sun is how many times greater than that of B from the sun?
5
4
3
2
