Gravitation Study Materials for Competitive Exams

Gravitation

Gravitational Potential & Field Newtons Law of Gravitation Satellite Motion

Q. If the Earth were to suddenly shrink to half its radius while maintaining its mass, what would happen to the gravitational force at its surface?

A. It would double
B. It would remain the same
C. It would become half
D. It would become four times stronger

Solution

The gravitational force at the surface is inversely proportional to the square of the radius. If the radius is halved, the force becomes four times stronger.

Correct Answer: D — It would become four times stronger

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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

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

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

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 creating the field?

A. -20 J/kg
B. -10 J/kg
C. 0 J/kg
D. -5 J/kg

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 infinity?

A. 0 J/kg
B. -10 J/kg
C. 10 J/kg
D. -5 J/kg

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 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

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 zero at infinity?

A. -10 J/kg
B. -5 J/kg
C. 0 J/kg
D. 10 J/kg

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

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 2 meters above the reference point?

A. -20 J/kg
B. -10 J/kg
C. 0 J/kg
D. -5 J/kg

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 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

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

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

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

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 a satellite is doubled while keeping its orbital radius constant, what happens to the gravitational force acting on it?

A. It doubles.
B. It remains the same.
C. It halves.
D. It quadruples.

Solution

The gravitational force acting on the satellite will double if its mass is doubled, as gravitational force is directly proportional to mass.

Correct Answer: A — It doubles.

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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

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

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

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.

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

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

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

Solution

Gravitational potential energy is directly proportional to mass, so it triples.

Correct Answer: A — It triples

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Q. If the mass of the Earth is 6 x 10^24 kg and the radius is 6.4 x 10^6 m, what is the gravitational force on a 1 kg mass at the surface?

A. 9.8 N
B. 6.67 N
C. 10 N
D. 8.9 N

Solution

Using F = G * (m1 * m2) / r^2, F = (6.67 x 10^-11) * (6 x 10^24 * 1) / (6.4 x 10^6)^2 = 9.8 N.

Correct Answer: A — 9.8 N

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Q. If the mass of the Earth is 6 x 10^24 kg and the radius is 6.4 x 10^6 m, what is the gravitational acceleration at the surface of the Earth?

A. 9.8 m/s²
B. 10 m/s²
C. 9.81 m/s²
D. 11 m/s²

Solution

Using g = G * M / R², where G = 6.67 x 10^-11 N m²/kg², M = 6 x 10^24 kg, and R = 6.4 x 10^6 m, we find g ≈ 9.8 m/s².

Correct Answer: A — 9.8 m/s²

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Q. If the mass of the Earth is 6 × 10^24 kg and its radius is 6.4 × 10^6 m, what is the acceleration due to gravity at its surface?

A. 9.8 m/s²
B. 10 m/s²
C. 9.81 m/s²
D. 8.9 m/s²

Solution

g = G * M / R² = (6.67 × 10^-11) * (6 × 10^24) / (6.4 × 10^6)² = 9.81 m/s²

Correct Answer: C — 9.81 m/s²

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Q. If the mass of the Earth is M and its radius is R, what is the gravitational acceleration at the surface of the Earth?

A. g = GM/R^2
B. g = GMR^2
C. g = G/MR^2
D. g = MR/G

Solution

The gravitational acceleration at the surface of the Earth is given by g = GM/R^2.

Correct Answer: A — g = GM/R^2

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Q. If the mass of the Earth is M and the radius is R, what is the gravitational acceleration at the surface of the Earth?

A. g = GM/R^2
B. g = GMR^2
C. g = G/R
D. g = M/R^2

Solution

The gravitational acceleration at the surface of the Earth is given by g = GM/R^2.

Correct Answer: A — g = GM/R^2

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Q. If the mass of the Earth is M and the radius is R, what is the gravitational force acting on a satellite of mass m at a height h?

A. GmM/R^2
B. GmM/(R+h)^2
C. GmM/(R-h)^2
D. GmM/h^2

Solution

The gravitational force F acting on a satellite at height h is given by F = GmM/(R+h)^2, where G is the gravitational constant.

Correct Answer: B — GmM/(R+h)^2

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Q. If the mass of the Earth were to double while its radius remained the same, what would happen to the gravitational acceleration at its surface?

A. It would double
B. It would remain the same
C. It would halve
D. It would increase by a factor of four

Solution

Gravitational acceleration is directly proportional to mass, so if the mass doubles, g also doubles.

Correct Answer: A — It would double

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Q. If the mass of the Earth were to double while its radius remains the same, what would happen to the gravitational acceleration at its surface?

A. It would double
B. It would remain the same
C. It would halve
D. It would increase by a factor of four

Solution

Gravitational acceleration is directly proportional to mass; thus, if the mass doubles, g also doubles.

Correct Answer: A — It would double

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Gravitation

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