Escape velocity, motion of a satellite, orbital velocity, time period and energy of a satellite - One Line Questions
1.
The total energy of a satellite in an elliptical orbit of semi-major axis a is: —
\( -GMa/(2a) \)
2.
The total energy of a satellite revolving in a circular orbit of radius r around the Earth is: —
\( -GMm/(2r) \)
3.
The kinetic energy of a satellite in a circular orbit of radius r is \( K \). Its potential energy is: —
\( -2K \)
4.
For a satellite in a circular orbit, the velocity is given by \( v_o = \sqrt{GM/(R+h)} \). The acceleration due to gravity at that height is \( g' = GM/(R+h)^2 \). The orbital velocity can also be written as: —
\( \sqrt{g'(R+h)} \)
5.
The orbital velocity of a satellite at a height h above the Earth's surface is given by: —
\( \sqrt{GM/(R+h)} \)
6.
The orbital velocity of a satellite is given by \( v_o = \sqrt{GM/(R+h)} \). If h approaches zero, the orbital velocity becomes: —
\( \sqrt{gR} \)
7.
The escape velocity from a planet of mass M and radius R is given by: —
\( \sqrt{2GM/R} \)
8.
The energy required to move a satellite from an orbit of radius \( r_1 \) to an orbit of radius \( r_2 \) (\( r_2 > r_1 \)) is: —
\( GMm(1/r_1 - 1/r_2) \)
9.
The escape velocity from the surface of a planet of radius R and mass M is \( v_e \). If the planet's radius is halved and its mass is doubled, the new escape velocity will be: —
\( 4 v_e \)
10.
The orbital speed of a satellite in a circular orbit of radius r around the Earth is \( v_o \). The escape speed from the same orbit is \( v_e \). The relation between them is: —
\( v_e = \sqrt{2} v_o \)
11.
The orbital velocity of a satellite in a circular orbit of radius R is \( v_o \). If the radius is increased to 2R, the new orbital velocity is: —
\( v_o / \sqrt{2} \)
12.
The ratio of escape velocity to orbital velocity for a satellite at the surface of the Earth is: —
\( \sqrt{2} \)
13.
A satellite is in a circular orbit of radius R. If it jumps to a circular orbit of radius 2R, the ratio of its new orbital velocity to the original orbital velocity is: —
1/\( \sqrt{2} \)
14.
The orbital radius of a satellite is R. If the radius of the orbit is increased to 4R, the time period of revolution will change by a factor of: —
8
15.
The kinetic energy of a satellite in a circular orbit of radius r is proportional to: —
1/r
16.
The potential energy of a satellite in a circular orbit of radius r is proportional to: —
-1/r
17.
A geostationary satellite orbits the Earth at a height of approximately: —
36000 km
18.
The time period of a satellite in a circular orbit of radius r is given by \( T = 2\pi \sqrt{r^3/(GM)} \). If the radius of the orbit is increased by a factor of 4, the time period will increase by a factor of: —
8
19.
If the escape velocity from the surface of the Earth is 11.2 km/s, the escape velocity from a planet of mass and radius double that of Earth is: —
22.4 km/s
20.
For a geostationary satellite, the time period of revolution is: —
24 hours
21.
What is the escape velocity of an object on the surface of the Earth? —
11.2 km/s
22.
The time period of a satellite orbiting close to the Earth's surface is approximately: —
85 minutes
23.
A satellite is in a circular orbit around the Earth. If its speed is increased, it will move to: —
An elliptical orbit
24.
Which of the following statements is true for a satellite in an elliptical orbit? —
Angular momentum is conserved
25.
The orbital velocity of a satellite is maximum when it is: —
At perigee
26.
If the distance of a satellite from the center of the Earth is doubled, its orbital velocity will: —
Become \( 1/\sqrt{2} \) times
27.
The total energy of a satellite in a circular orbit of radius r is E. If the radius is increased to 2r, the new total energy will be: —
E/2
28.
For a geostationary satellite, the angular velocity is: —
Equal to the angular velocity of Earth's rotation
29.
A satellite is orbiting the Earth in a circular orbit. If its speed is reduced by 10%, it will: —
Fall to Earth
30.
A satellite is revolving around a planet in a circular orbit. If the velocity of the satellite is suddenly increased by 50%, it will: —
Escape from the orbit
31.
A satellite is in a circular orbit of radius r. If the gravitational force were suddenly removed, the satellite would: —
Move in a straight line tangent to the orbit
32.
If the radius of Earth were to decrease by 1%, its mass remaining the same, then the escape velocity would: —
Increase by 0.5%
33.
A satellite is in a circular orbit. If the radius of the orbit increases, the orbital velocity: —
Decreases
34.
What is the condition for a satellite to be in a geostationary orbit? —
All of the above
35.
For a satellite in a circular orbit, the kinetic energy is K. The total energy is: —
-K
36.
For a satellite to orbit the Earth, its orbital velocity must be: —
Less than escape velocity
37.
Which of the following is conserved for a satellite in an elliptical orbit around the Earth? —
Angular momentum about the Earth's center
38.
The orbital velocity of a satellite is independent of: —
Mass of the satellite
39.
If a satellite is in an elliptical orbit, its speed is: —
Maximum at perigee
40.
The minimum velocity with which a body must be projected vertically upwards from the surface of the Earth to escape Earth's gravitational field is called: —
Escape velocity
41.
A satellite is launched into a circular orbit of radius R around the Earth. To transfer it to a circular orbit of radius 2R, the energy required is: —
Positive
42.
If a satellite is moved from a lower orbit to a higher orbit, its: —
Total energy increases
43.
If a satellite is in an orbit of radius r, its kinetic energy is proportional to: —
1/r
44.
The time period of a satellite in a circular orbit of radius r is proportional to: —
r^{3/2}
45.
The escape velocity from a planet of radius R and density \( \rho \) is proportional to: —
R \( \sqrt{\rho} \)
46.
If the Earth suddenly shrinks to half its radius without changing its mass, the escape velocity from the surface will: —
Become double
47.
For a satellite in a circular orbit, the time period T is related to the orbital radius r by: —
T \( \propto r^{3/2} \)
48.
A satellite is in an elliptical orbit. Its speed at perigee is greater than its speed at apogee because: —
The distance from Earth is smaller at perigee
49.
Escape velocity depends on the mass of: —
The celestial body from which it is projected
50.
A satellite is in a circular orbit of radius R. If its energy is increased by \( \Delta E \), it moves to a higher orbit. The change in angular momentum is: —
Depends on the new orbit