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
The largest and the shortest distance of the earth from the sun are r1 and r2. Its distance from the sun when it is perpendicular to the major axis of the orbit drawn from the sun is
The density of newly discovered planet is twice that of earth.The acceleration due to gravity at the surface of the planet is equal to that at the surface of the earth. If the radius of the earth is R, the radius of the planet would be
2R
4R
R/2
R/4
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
What will be the formula of the mass in terms of g, R and G? (R = radius of earth)
g2 R/G
G R2/g
G R/g
g R2/G
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
The escape velocity from earth is 11.2 km/s. If a body is to be projected in a direction making an angle 45o to the vertical, then the escape velocity is
11.2 × 2 km/s
11.2 km/s
11.2/√2 km/s
11.2√2 km/s
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
If the gravitational force between two objects were proportional to 1/R (and not as 1/R2), where R is separation between them, then a particle in circular orbit under such a force would have its orbital speed v proportional to
1/R2
R0
R
1/R
For a satellite escape velocity is 11 km/s. If the satellite is launched at an angle of 60o with the vertical, then escape velocity will be
11 Km/s
11√3 Km/s
11/√3 Km/s
33 Km/s