The change in the value of g at a height h above the surface of the earth is the same as at a depth d below that surface of earth. When both d and h are much smaller than the radius of earth, then, d = αh. Find the value of α.
The gravitational field inside the earth is given by where r is the distance from centre
The correct answer is: 2
Energy required to move a body of mass m from an orbit of radius 2R to 3R is Find the value of α
The correct answer is: 12
A satellite in a circular orbit of radius r has time period of 4hrs. A satellite with orbital radius of 4r around the same planet will have a time period of in hours.
Radius of orbit of the first satellite
R1 = R
Time period of the first satellite T = 4 hrs. and radius of orbit of second satellite = 4r
The time period of satellite is given by
The correct answer is: 32
The minimum and maximum distances of a satellite from the centre of earth are 2R and 4R respectively, where R is the radius of earth and M is the mass of the earth. The radius of curvature at the point of minimum distance is λR. Find the value of λ.
Applying conservation of angular momentum
From conservation of energy
Solving Eqs. (1) and (2), we get
If r is the radius of curvature at point A
The correct answer is: 2.667
Maximum height reached by a rocket fired with a speed equal to 50% of the escape velocity from Earth’s surface is R/α. Find the value of α.
Applying energy conservation
The correct answer is: 3
Two satellites S1 and S2 of equal masses revolves in the same sense around a heavy planet in coplanar circular orbit of radii R and 4R. Find the value of
⇒ V1/V2 = (4/1)1/2
⇒ V1/V2 = 2/1
Radius of the earth is R and the means density is ρ. Find out the gravitational potential at the earth’s surface απGρR2. Find the value of α.
The correct answer is: -1.333
A body which is initially at rest at a height R above the surface of the earth of radius R, falls freely towards the earth. Find out its velocity (in m/s) on reaching the surface of earth.
Take g = 10m/s2 and R = 6400km.
Potential energy at ground surface
potential energy at a height of R is
When a body comes to ground
Loss in potential energy = Gain in kinetic energy
The correct answer is: 8000
A particle is projected from the surface of earth with an initial speed of 4.0km/s. Find the maximum height (in kms) attained by the particle.
Radius of earth = 6400km and the maximum height attained by the particle is, and g = 9.8 m/s2.
Substituting the value,
or h = 935km
The correct answer is: 935
The orbital velocity of an artificial satellite in a circular orbit just above the earth’s surface is V0. The value of orbital velocity for another satellite orbiting at an altitude of half of earth’s radius is Find the value of α.
For first satellite
For second satellite
The correct answer is: 0.667