Question
The gravitational force of attraction between two identical masses is 36 N when the masses are separated by a distance of 3 m. If the distance between them is reduced to 1 m, which of the following is true about the net gravitational field strength due to both masses being at the halfway point?
(A) It is 9 times stronger total.
(B) Not enough information is given to determine net gravitational field strength.
(C) Each mass’s gravitation is 9 times stronger, so the net gravitational field strength is 18 times stronger.
(D) It is zero.
▶️Answer/Explanation
Ans:(D) Gravitational field strength halfway between any two equal masses is always zero as each contributes oppositely directed gravitational fields.
Question
If it takes 5 N to move 2 C of charge in a constant electric field, how much energy is needed to move 3 C of charge 40 cm in the same field?
(A) 2.5 J
(B) 7.5 J
(C) 2.0 J
(D) 3.0 J
▶️Answer/Explanation
Ans: (D) First, find the electric field strength:
E = F / q = 5/2 N/C
Now, find the work done:
W = F · D = qE · D = (3C)(5/2)(0.4 m) = 3 J
Question
Which of the following expressions is equivalent to the magnitude of the escape velocity in terms of the magnitude of the orbital velocity v for a spacecraft?
(A) \(2v\)
(B) \(v\)
(C) \(4v\)
(D) \(\sqrt{2}v\)
▶️Answer/Explanation
Ans:(D) Orbital velocity: \(F_{g}= centripetal force = mv^{2}/R\)
\( GMm/R^{2}=mv^{2}/R\)
\( v=(GM/R)^{1/2}\)\(
Escape velocity: \( E_{total}>0\)
\(KE+PE>0\)
\( \frac{1}{2}mv^{2}=GMm/R>0\) (using universal gravitational PE)
\(v>(2GM/R)^{1/2}\)
Question
Which of the following graphs correctly shows the relationship between magnitude of gravitational force and distance between two masses?
(A) 
(B) 
(C) 
(D) 
▶️Answer/Explanation
Ans:(B) The gravitational force between two masses has a \(1/R^{2}\) relationship (where R is the distance from center to center). Graph B shows the correct inverse relationship.
Question
Compare the force experienced by an electron in the two situations shown above. In the situation on the left, the electron is a distance D from a positive charge Q . In the situation on the right, the electron is 3 times farther (3 D ) from 3 times as much positive charge (3 Q ) as in the scenario on the left. The force of electrical attraction in the scenario on the right will
(A) remain the same as the situation on the left
(B) be 3 times stronger than the situation on the left
(C) be 3 times weaker than the situation on the left
(D) be 9 times weaker than the situation on the left
▶️Answer/Explanation
Ans: (C)
Coulomb’s law is \(kQ_{1}Q_{2}/R^{2}\). Tripling \(Q_{1}\) triples the force. Tripling R makes the force 9 times weaker. Net effect: 3 × 1/9 = 1/3