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
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.
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.
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.
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.
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.
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.
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.
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.
