Gravitational Potential & Field
Q. If the mass of an object is 10 kg and it is located at a point where the gravitational potential is -30 J/kg, what is the gravitational potential energy of the object?
A.
-300 J
B.
-30 J
C.
300 J
D.
30 J
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Solution
Gravitational potential energy U = m * V = 10 * (-30) = -300 J.
Correct Answer: A — -300 J
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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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Q. If the mass of an object is doubled, how does its gravitational potential energy change at a constant height?
A.
It remains the same
B.
It doubles
C.
It halves
D.
It quadruples
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Solution
The gravitational potential energy U = mgh will double if the mass m is doubled at constant height h.
Correct Answer: B — It doubles
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Q. If the mass of an object is halved and the distance from the center of the Earth is doubled, what happens to the gravitational potential energy?
A.
It remains the same.
B.
It doubles.
C.
It halves.
D.
It quadruples.
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Solution
Gravitational potential energy is directly proportional to mass and inversely proportional to distance, so it halves.
Correct Answer: C — It halves.
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Q. If the mass of an object is halved, how does its gravitational potential energy change at a constant height?
A.
It doubles
B.
It halves
C.
It remains the same
D.
It becomes zero
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Solution
The gravitational potential energy U = mgh is directly proportional to the mass, so if the mass is halved, the potential energy also halves.
Correct Answer: B — It halves
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Q. If the mass of an object is tripled, how does its gravitational potential energy change at a constant height?
A.
It triples
B.
It doubles
C.
It remains the same
D.
It increases by a factor of nine
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Solution
Gravitational potential energy U = mgh, so if mass is tripled, U also triples.
Correct Answer: A — It triples
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Q. If the mass of an object is tripled, how does the gravitational potential energy change for a constant height?
A.
It triples
B.
It doubles
C.
It halves
D.
It remains the same
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Solution
Gravitational potential energy is directly proportional to mass, so it triples.
Correct Answer: A — It triples
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Q. In a gravitational field, the potential energy of an object is maximum at which point?
A.
At the surface of the Earth
B.
At infinity
C.
At the center of the Earth
D.
At the highest point in the field
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Solution
The gravitational potential energy is considered maximum at infinity, where it is defined to be zero.
Correct Answer: B — At infinity
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Q. The gravitational field inside a uniform spherical shell is:
A.
Zero
B.
Constant
C.
Increases linearly
D.
Decreases linearly
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Solution
The gravitational field inside a uniform spherical shell is zero.
Correct Answer: A — Zero
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Q. The gravitational field strength at the surface of a planet is 9.8 N/kg. What is the gravitational potential at the surface if the radius of the planet is 6.4 x 10^6 m?
A.
-62.72 x 10^6 J/kg
B.
-9.8 J/kg
C.
-19.6 x 10^6 J/kg
D.
-39.2 x 10^6 J/kg
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Solution
V = -g * r = -9.8 N/kg * 6.4 x 10^6 m = -62.72 x 10^6 J/kg.
Correct Answer: A — -62.72 x 10^6 J/kg
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Q. The gravitational field strength at the surface of the Earth is approximately 9.8 N/kg. What is the gravitational potential at the surface of the Earth?
A.
0 J/kg
B.
-9.8 J/kg
C.
-19.6 J/kg
D.
-39.2 J/kg
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Solution
The gravitational potential at the surface of the Earth is negative, approximately -9.8 J/kg.
Correct Answer: B — -9.8 J/kg
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Q. The gravitational potential at a point is defined as the work done in bringing a unit mass from infinity to that point. What is the unit of gravitational potential?
A.
J/kg
B.
N/kg
C.
J/m
D.
N/m
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Solution
The unit of gravitational potential is Joules per kilogram (J/kg).
Correct Answer: A — J/kg
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Q. The gravitational potential at infinity is defined as what value?
A.
0
B.
1
C.
-1
D.
Undefined
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Solution
The gravitational potential at infinity is defined to be 0.
Correct Answer: A — 0
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Q. The gravitational potential energy of a system of two masses is negative. What does this imply?
A.
The masses are repelling each other
B.
The masses are attracting each other
C.
The system is in equilibrium
D.
The potential energy is zero
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Solution
A negative gravitational potential energy indicates that the masses are attracting each other.
Correct Answer: B — The masses are attracting each other
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Q. The gravitational potential energy of an object at height h is given by which formula?
A.
mgh
B.
gh
C.
mg/h
D.
mgh^2
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Solution
The gravitational potential energy U at height h is given by U = mgh.
Correct Answer: A — mgh
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Q. The gravitational potential energy of an object is given by which formula?
A.
U = mgh
B.
U = -GMm/r
C.
U = 1/2 mv^2
D.
U = Fd
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Solution
The gravitational potential energy U of an object in a gravitational field is given by U = -GMm/r.
Correct Answer: B — U = -GMm/r
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Q. The gravitational potential energy of two masses m1 and m2 separated by a distance r is given by which formula?
A.
-G(m1*m2)/r
B.
G(m1*m2)/r
C.
-G(m1+m2)/r
D.
G(m1+m2)/r
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Solution
The gravitational potential energy U = -G(m1*m2)/r.
Correct Answer: A — -G(m1*m2)/r
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Q. What happens to the gravitational potential as you move away from a mass?
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 mass.
Correct Answer: B — It decreases
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Q. What happens to the gravitational potential as you move away from a massive body?
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 massive body.
Correct Answer: B — It decreases
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Q. What happens to the gravitational potential energy of an object as it moves away from a planet?
A.
It increases.
B.
It decreases.
C.
It remains constant.
D.
It becomes zero.
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Solution
As an object moves away from a planet, its gravitational potential energy increases (becomes less negative).
Correct Answer: A — It increases.
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Q. What happens to the gravitational potential energy of an object as it moves away from the Earth?
A.
It increases.
B.
It decreases.
C.
It remains constant.
D.
It becomes zero.
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Solution
As an object moves away from the Earth, its gravitational potential energy increases.
Correct Answer: A — It increases.
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Q. What is the gravitational field strength at a distance 'R' from the center of a planet of radius 'R' and uniform density?
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Solution
Inside a uniform sphere, the gravitational field strength varies linearly with distance from the center, so at R/2 it is g/2.
Correct Answer: C — g/2
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Q. What is the gravitational field strength at the surface of a planet of mass M and radius R?
A.
GM/R^2
B.
2GM/R^2
C.
GM/R
D.
G/R^2
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Solution
The gravitational field strength g at the surface of a planet is given by g = GM/R^2.
Correct Answer: A — GM/R^2
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Q. What is the gravitational field strength at the surface of the Earth?
A.
9.8 N/kg
B.
10 N/kg
C.
11 N/kg
D.
12 N/kg
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Solution
The gravitational field strength at the surface of the Earth is approximately 9.8 N/kg.
Correct Answer: A — 9.8 N/kg
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Q. What is the gravitational potential at a distance 'r' from a mass 'M'?
A.
-GM/r
B.
-GM/r^2
C.
GM/r
D.
GM/r^2
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Solution
The gravitational potential V at a distance r from a mass M is given by V = -GM/r.
Correct Answer: A — -GM/r
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Q. What is the gravitational potential at a distance 'r' from a point mass 'M'?
A.
-GM/r
B.
-GM/r^2
C.
GM/r
D.
GM/r^2
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Solution
The gravitational potential V at a distance r from a point mass M is given by V = -GM/r.
Correct Answer: A — -GM/r
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Q. What is the gravitational potential at a point infinitely far away from a mass?
A.
Zero
B.
Positive
C.
Negative
D.
Undefined
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Solution
The gravitational potential at a point infinitely far away from a mass is defined to be zero.
Correct Answer: A — Zero
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Q. What is the gravitational potential at infinity?
A.
Zero
B.
Positive
C.
Negative
D.
Undefined
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Solution
The gravitational potential at infinity is defined to be zero.
Correct Answer: A — Zero
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Q. What is the gravitational potential energy of a 10 kg mass at a height of 5 m above the ground?
A.
50 J
B.
100 J
C.
0 J
D.
10 J
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Solution
The gravitational potential energy is calculated using the formula U = mgh = 10 kg * 9.8 m/s² * 5 m = 490 J.
Correct Answer: B — 100 J
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Q. What is the gravitational potential energy of a 2 kg mass at a height of 5 m?
A.
10 J
B.
20 J
C.
30 J
D.
40 J
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Solution
Using U = mgh, U = 2 kg * 9.8 m/s^2 * 5 m = 98 J.
Correct Answer: B — 20 J
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