Gravitational Potential & Field
Q. What is the gravitational potential energy of a 5 kg mass at a height of 10 m above the ground?
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A.
490 J
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B.
500 J
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C.
510 J
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D.
450 J
Solution
Gravitational potential energy U = mgh = 5 * 9.8 * 10 = 490 J.
Correct Answer: B — 500 J
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Q. What is the gravitational potential energy of a mass 'm' at height 'h' above the Earth's surface?
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A.
mgh
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B.
mg/h
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C.
gh/m
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D.
mgh^2
Solution
The gravitational potential energy U at height h is given by U = mgh.
Correct Answer: A — mgh
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Q. What is the gravitational potential energy of a mass of 10 kg at a height of 5 m in a gravitational field of strength 9.8 N/kg?
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A.
490 J
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B.
50 J
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C.
98 J
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D.
0 J
Solution
Gravitational potential energy U = mgh = 10 * 9.8 * 5 = 490 J.
Correct Answer: A — 490 J
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Q. What is the relationship between gravitational field strength and gravitational potential?
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A.
Field strength is the gradient of potential.
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B.
Field strength is the integral of potential.
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C.
They are independent.
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D.
Field strength is the square of potential.
Solution
Gravitational field strength is the negative gradient of gravitational potential.
Correct Answer: A — Field strength is the gradient of potential.
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Q. What is the relationship between gravitational potential and gravitational field strength?
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A.
V = -g * r
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B.
g = -dV/dr
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C.
V = g * r
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D.
g = dV/dr
Solution
The gravitational field strength g is the negative gradient of the gravitational potential V, given by g = -dV/dr.
Correct Answer: B — g = -dV/dr
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Q. What is the shape of the equipotential surfaces around a point mass?
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A.
Straight lines
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B.
Parabolas
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C.
Spheres
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D.
Cylinders
Solution
The equipotential surfaces around a point mass are spherical.
Correct Answer: C — Spheres
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Q. What is the shape of the gravitational field lines around a point mass?
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A.
Straight lines
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B.
Curved lines
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C.
Concentric circles
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D.
Radial lines
Solution
The gravitational field lines around a point mass are radial, pointing towards the mass.
Correct Answer: D — Radial lines
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Q. What is the unit of gravitational potential?
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A.
J/kg
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B.
N/kg
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C.
J
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D.
kg
Solution
The unit of gravitational potential is Joules per kilogram (J/kg).
Correct Answer: A — J/kg
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Q. What is the work done in moving a mass from a point A to point B in a uniform gravitational field?
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A.
Depends on the path taken
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B.
Zero
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C.
Equal to the change in gravitational potential energy
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D.
Equal to the gravitational force times distance
Solution
The work done is equal to the change in gravitational potential energy, which depends on the initial and final positions.
Correct Answer: C — Equal to the change in gravitational potential energy
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Q. What is the work done in moving an object from a point A to point B in a uniform gravitational field?
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A.
Depends on the path taken
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B.
Zero
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C.
Depends on the mass of the object
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D.
Depends on the height difference
Solution
The work done in moving an object in a uniform gravitational field depends only on the height difference between points A and B.
Correct Answer: D — Depends on the height difference
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Q. What is the work done in moving an object from one point to another in a gravitational field?
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A.
Depends on the path taken
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B.
Is always zero
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C.
Depends only on the initial and final positions
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D.
Is maximum at the highest point
Solution
The work done in moving an object in a gravitational field depends only on the initial and final positions, not the path taken.
Correct Answer: C — Depends only on the initial and final positions
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Q. Which of the following correctly describes gravitational field lines?
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A.
They point away from the mass.
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B.
They are always straight lines.
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C.
They never intersect.
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D.
They can be closed loops.
Solution
Gravitational field lines never intersect because it would imply two different gravitational forces acting on the same point.
Correct Answer: C — They never intersect.
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Q. Which of the following correctly describes gravitational potential energy?
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A.
It is a scalar quantity.
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B.
It is a vector quantity.
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C.
It can be negative.
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D.
Both A and C.
Solution
Gravitational potential energy is a scalar quantity and can be negative when the object is within the gravitational field of another mass.
Correct Answer: D — Both A and C.
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Q. Which of the following correctly describes the relationship between gravitational potential and gravitational field?
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A.
Potential is the derivative of field.
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B.
Field is the derivative of potential.
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C.
Both are independent.
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D.
They are equal.
Solution
The gravitational field is the negative gradient of gravitational potential.
Correct Answer: B — Field is the derivative of potential.
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Q. Which of the following statements about gravitational potential energy is true?
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A.
It is always positive.
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B.
It can be negative.
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C.
It is independent of the reference point.
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D.
It increases with distance.
Solution
Gravitational potential energy can be negative depending on the reference point chosen.
Correct Answer: B — It can be negative.
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Q. Which of the following statements is true about gravitational field lines?
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A.
They are straight lines
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B.
They can cross each other
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C.
They point towards the mass
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D.
They are always circular
Solution
Gravitational field lines point towards the mass creating the field.
Correct Answer: C — They point towards the mass
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Q. Which of the following statements is true about gravitational potential energy?
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A.
It is always positive.
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B.
It can be negative.
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C.
It is independent of position.
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D.
It is always zero.
Solution
Gravitational potential energy can be negative depending on the reference point chosen.
Correct Answer: B — It can be negative.
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