AP Physics C Mechanics Gravitational Force MCQ

Gravitational Force AP  Physics C Mechanics MCQ – Exam Style Questions etc.

Gravitational Force AP  Physics C Mechanics MCQ

Unit 2: Force and Translational Dynamics

Weightage : 20-15%

AP Physics C Mechanics Exam Style Questions – All Topics

Question

Two moons of equal mass are in circular orbits around a planet. Moon 1 orbits with a radius of r and moon 2 orbits with a radius of 3r. What is the ratio of the magnitude of the planet’s gravitational force on moon 2 to that on moon 1, \(F_{G(on2)}/F_{G(0n1)}\) ?
(A) 9/1
(B) 3/ 1
(C) 1/1
(D) 1/ 3
(E) 1/ 9

Answer/Explanation

Ans:E

Question

 The escape speed for a rocket at Earth’s surface is \(v_e\). What would be the rocket’s escape speed from the surface of a planet with twice Earth’s mass and the same radius as Earth?

(A)\(2v_e\)

(B)\(\sqrt{2v_e}\)

(C)\(v_e\)

(D)\(\frac{v_e}{\sqrt{2}}\)

(E)\(\frac{v_e}{2}\)

Answer/Explanation

Ans:B

Question

26. Spheres X, Y, and Z have the masses and locations indicated in the figure above. What is  the magnitude of the net gravitational force on sphere X due to the other two spheres?

(A)\(\frac{Gm^2}{2r^2}\)
(B)\(\frac{Gm^2}{r^2}\)
(C)\(\frac{11Gm^2}{9r^2}\)
(D)\(\frac{5Gm^2}{4r^2}\)
(E)\(\frac{2Gm^2}{r^2}\)

Answer/Explanation

Ans:C

Both sphere Y and Z will attract sphere X to the right. Adding the force of gravity from both spheres together and substituting into the equation for gravitational force yields

Questions (a)-(b)

Two identical satellites orbit a planet of radius R in circular orbits A and C of radii 3R and 12R, respectively, as shown above.

Question(a)

How does the magnitude of the gravitational force \(F_A\) between the planet and satellite in  orbit A compare to the magnitude of the gravitational force\( F_C\) between the planet and satellite in orbit C?
(A) \(F_A = 2F_C \)

(B) \(F _A= 3F_C \)

(C)\( F_A = 4F_C \)

(D) \(F_ A = 12F_C\)

(E) \(F_ A = 16F_C\)

Answer/Explanation

Ans:E

Substituting into the equation for the gravitational force on the satellite in orbit A yields     

Substituting into the equation for the gravitational force on the

Question(b)

 The speed of the satellite in orbit A is \(v_A\) . The speed of the satellite in orbit C is \(v_C\). The ratio \(v_A/ v_C\) is
(A) 1 /2
(B) 1/1
(C) 2/1
(D) 4/1
(E)12/ 1

Answer/Explanation

Ans:C

Setting the centripetal force equal to the gravitational force\( F_c=F_g\)

and solving for the speed of satellite A yields   \(\frac{m_Av^2_A}{r_A}=\frac{GMm_A}{r^2_A}\)
\(v_A=\frac{GM}{r_A}\)

\(F_C=F_g\)

Repeating for satellite C yields\( \frac{m_Av^2_A}{r_A}=\frac{GMm_A}{r^2_c}
v_C=\frac{GM}{r_c}\). Taking the ratio  of the two speeds yields  \(\frac{v_A}{v_C}=\frac{\frac{GM}{r_A}}{\frac{GM}{r_c}} =\sqrt{\frac{r_c}{r_A}}=\sqrt{\frac{12R}{3R}}=\frac{2}{1}\)

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