AP Physics 1 Question 266: Answer and Explanation

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Question: 266

2. Two 1 kg spheres each carry a charge of magnitude 1 C. How does FE, the strength of the electric force between the spheres, compare to FG, the strength of their gravitational attraction?

  • A. FE < FG
  • B. FE = FG
  • C. FE > FG
  • D. If the charges on the spheres are of the same sign, then FE > FG; but if the charges on the spheres are of the opposite sign, then FE < FG.

Correct Answer: C

Explanation:

C

The strength of the electric force is given by kq2/r2, and the strength of the gravitational force is Gm2/r2. Since both of these quantities have r2 in the denominator, you simply need to compare the numerical values of kq2 and Gm2. There's no contest. Since

kq2 = (9 × 109 N·m2/C2)(1 C)2 = 9 × 109 N·m2

and

Gm2 = (6.7 × 10-11 N·m2/kg2)(1 kg)2 = 6.7 × 10-11 N·m2

you can see that kq2 > Gm2, so FE is much stronger than FG.