Gravitational Potential & Field
Q. A mass 'm' is lifted to a height 'h' above the Earth's surface. What is the change in gravitational potential energy?
A.
mgh
B.
mg(h + R)
C.
mgR
D.
0
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Solution
The change in gravitational potential energy when a mass m is lifted to a height h is given by ΔU = mgh.
Correct Answer: A — mgh
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Q. A mass m is lifted to a height h in a uniform gravitational field. What is the work done against gravity?
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Solution
The work done against gravity when lifting a mass m to a height h is given by W = mgh.
Correct Answer: A — mgh
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Q. A satellite is in a circular orbit around the Earth. What happens to its gravitational potential energy as it moves to a higher orbit?
A.
It increases.
B.
It decreases.
C.
It remains constant.
D.
It becomes zero.
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Solution
As the satellite moves to a higher orbit, its distance from the Earth increases, leading to an increase in gravitational potential energy.
Correct Answer: A — It increases.
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Q. A satellite is in a circular orbit around the Earth. What is the gravitational potential energy of the satellite?
A.
It is positive.
B.
It is negative.
C.
It is zero.
D.
It is constant.
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Solution
The gravitational potential energy of a satellite in orbit is negative due to the attractive force of gravity.
Correct Answer: B — It is negative.
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Q. At what distance from a mass M does the gravitational potential become zero?
A.
At infinity
B.
At the surface of the mass
C.
At 1 meter
D.
At 2 meters
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Solution
The gravitational potential becomes zero at infinity, as V approaches zero as r approaches infinity.
Correct Answer: A — At infinity
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Q. At what point in a gravitational field is the gravitational potential constant?
A.
At the center of the mass
B.
At infinity
C.
Along an equipotential surface
D.
At the surface of the mass
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Solution
The gravitational potential is constant along an equipotential surface.
Correct Answer: C — Along an equipotential surface
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Q. At what point in space is the gravitational potential energy of an object zero?
A.
At the center of the Earth
B.
At infinity
C.
At the surface of the Earth
D.
At the Moon
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Solution
The gravitational potential energy is considered zero at infinity.
Correct Answer: B — At infinity
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Q. At what point in space is the gravitational potential zero?
A.
At the center of the Earth.
B.
At infinity.
C.
At the surface of the Earth.
D.
At the center of the Moon.
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Solution
The gravitational potential is considered zero at infinity.
Correct Answer: B — At infinity.
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Q. How does the gravitational field strength vary with distance from a point mass?
A.
It increases linearly.
B.
It decreases with the square of the distance.
C.
It remains constant.
D.
It decreases linearly.
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Solution
The gravitational field strength decreases with the square of the distance from the point mass.
Correct Answer: B — It decreases with the square of the distance.
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Q. How does the gravitational potential change as you move away from a planet?
A.
It increases.
B.
It decreases.
C.
It remains constant.
D.
It oscillates.
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Solution
The gravitational potential decreases as you move away from a planet.
Correct Answer: B — It decreases.
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Q. How does the gravitational potential energy of a system of two masses change as they move closer together?
A.
It increases.
B.
It decreases.
C.
It remains constant.
D.
It becomes zero.
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Solution
The gravitational potential energy decreases as the two masses move closer together.
Correct Answer: B — It decreases.
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Q. How does the gravitational potential energy of an object change when it is lifted to a height 'h' above the ground?
A.
It decreases.
B.
It increases.
C.
It remains the same.
D.
It becomes zero.
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Solution
The gravitational potential energy increases as the object is lifted to a height 'h' above the ground.
Correct Answer: B — It increases.
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Q. If the distance from a mass is doubled, how does the gravitational field strength change?
A.
It doubles.
B.
It halves.
C.
It becomes one-fourth.
D.
It becomes one-eighth.
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Solution
The gravitational field strength is inversely proportional to the square of the distance, so it becomes one-fourth.
Correct Answer: C — It becomes one-fourth.
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Q. If the distance from the center of the Earth is doubled, how does the gravitational potential change?
A.
It doubles.
B.
It halves.
C.
It becomes zero.
D.
It quadruples.
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Solution
The gravitational potential is inversely proportional to the distance, so if the distance is doubled, the potential halves.
Correct Answer: B — It halves.
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Q. If the distance from the center of the Earth is doubled, how does the gravitational field strength change?
A.
It doubles.
B.
It halves.
C.
It becomes zero.
D.
It quadruples.
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Solution
The gravitational field strength varies inversely with the square of the distance, so if the distance is doubled, the field strength becomes 1/4.
Correct Answer: B — It halves.
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Q. If the distance from the center of the Earth is doubled, what happens to the gravitational field strength?
A.
It doubles.
B.
It halves.
C.
It becomes one-fourth.
D.
It becomes zero.
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Solution
The gravitational field strength varies inversely with the square of the distance from the center of the Earth, so if the distance is doubled, the field strength becomes one-fourth.
Correct Answer: C — It becomes one-fourth.
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Q. If the gravitational field strength at a point is 10 N/kg, what is the gravitational potential at that point, assuming it is 2 meters above the reference point?
A.
-20 J/kg
B.
-10 J/kg
C.
0 J/kg
D.
-5 J/kg
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Solution
Gravitational potential V = -g * h = -10 N/kg * 2 m = -20 J/kg.
Correct Answer: A — -20 J/kg
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Q. If the gravitational field strength at a point is 10 N/kg, what is the gravitational potential at that point assuming it is at infinity?
A.
0 J/kg
B.
-10 J/kg
C.
10 J/kg
D.
-5 J/kg
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Solution
The gravitational potential is negative and is given by V = -g * r. At infinity, V approaches 0, so at a field strength of 10 N/kg, V = -10 J/kg.
Correct Answer: B — -10 J/kg
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Q. If the gravitational field strength at a point is 10 N/kg, what is the gravitational potential at that point assuming it is zero at infinity?
A.
-10 J/kg
B.
-5 J/kg
C.
0 J/kg
D.
10 J/kg
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Solution
The gravitational potential V is related to the gravitational field strength g by V = -g * r. If we consider r to be 1 meter, V = -10 * 1 = -10 J/kg.
Correct Answer: A — -10 J/kg
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Q. If the gravitational field strength at a point is 10 N/kg, what is the gravitational potential at that point assuming it is at a distance of 2 m from the mass?
A.
-20 J/kg
B.
-10 J/kg
C.
0 J/kg
D.
-5 J/kg
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Solution
Gravitational potential V = -g * r = -10 * 2 = -20 J/kg.
Correct Answer: A — -20 J/kg
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Q. If the gravitational field strength at a point is 10 N/kg, what is the gravitational potential at that point, assuming it is at a distance of 2 m from the mass creating the field?
A.
-20 J/kg
B.
-10 J/kg
C.
0 J/kg
D.
-5 J/kg
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Solution
Gravitational potential V = -g * r = -10 N/kg * 2 m = -20 J/kg.
Correct Answer: A — -20 J/kg
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Q. If the gravitational field strength at a point is 10 N/kg, what is the gravitational potential at that point, assuming it is at a distance of 2 meters from the mass creating the field?
A.
-20 J/kg
B.
-10 J/kg
C.
0 J/kg
D.
-5 J/kg
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Solution
Gravitational potential V = -g * r = -10 N/kg * 2 m = -20 J/kg.
Correct Answer: A — -20 J/kg
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Q. If the gravitational field strength at a point is 10 N/kg, what is the gravitational potential at that point, assuming it is 2 meters from the mass creating the field?
A.
-20 J/kg
B.
-10 J/kg
C.
0 J/kg
D.
-5 J/kg
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Solution
Gravitational potential V = -g * r = -10 N/kg * 2 m = -20 J/kg.
Correct Answer: A — -20 J/kg
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Q. If the gravitational field strength at a point is 10 N/kg, what is the gravitational potential at that point assuming the reference point is at infinity?
A.
-10 J/kg
B.
10 J/kg
C.
0 J/kg
D.
-5 J/kg
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Solution
The gravitational potential V is related to the gravitational field strength g by V = -g * r. If we consider r to be 1 meter, V = -10 * 1 = -10 J/kg.
Correct Answer: A — -10 J/kg
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Q. If the gravitational field strength at a point is 10 N/kg, what is the gravitational potential at that point assuming it is 2 meters from the mass?
A.
-20 J/kg
B.
-10 J/kg
C.
0 J/kg
D.
-5 J/kg
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Solution
Gravitational potential V = -g * r = -10 * 2 = -20 J/kg.
Correct Answer: A — -20 J/kg
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Q. If the gravitational potential at a point is -15 J/kg and the gravitational field strength is constant at 3 N/kg, what is the distance from the mass?
A.
5 m
B.
10 m
C.
15 m
D.
20 m
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Solution
Using V = -g * r, we have -15 = -3 * r, thus r = 15/3 = 5 m.
Correct Answer: B — 10 m
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Q. If the gravitational potential at a point is -20 J/kg and the gravitational field strength is 4 N/kg, what is the distance from the mass?
A.
5 m
B.
10 m
C.
15 m
D.
20 m
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Solution
Using V = -g * r, we have -20 = -4 * r, thus r = 20/4 = 5 m.
Correct Answer: B — 10 m
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Q. If the gravitational potential at a point is -30 J/kg and the gravitational field strength is 5 N/kg, what is the distance from the mass?
A.
6 m
B.
3 m
C.
5 m
D.
4 m
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Solution
Using V = -g * r, we have -30 = -5 * r, thus r = 30/5 = 6 m.
Correct Answer: B — 3 m
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Q. If the gravitational potential at a point is -30 J/kg, what is the gravitational field strength at that point?
A.
3 N/kg
B.
30 N/kg
C.
0 N/kg
D.
Cannot be determined
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Solution
The gravitational field strength can be found using the relation E = -dV/dr. If V = -30 J/kg, E = 3 N/kg.
Correct Answer: A — 3 N/kg
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Q. If the mass of an object is 5 kg and it is at a height of 10 m above the ground, what is its gravitational potential energy?
A.
50 J
B.
100 J
C.
500 J
D.
0 J
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Solution
Gravitational potential energy U = mgh = 5 * 10 * 10 = 500 J.
Correct Answer: B — 100 J
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