**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 *F*_{E}, the strength of the electric force between the spheres, compare to *F*_{G}, the strength of their gravitational attraction?

- A.
*F*_{E}<*F*_{G} - B.
*F*_{E}=*F*_{G} - C.
*F*_{E}>*F*_{G} - D. If the charges on the spheres are of the same sign, then
*F*_{E}>*F*_{G}; but if the charges on the spheres are of the opposite sign, then*F*_{E}<*F*_{G}.

**Correct Answer:** C

**Explanation:**

**C**

The strength of the electric force is given by *kq*^{2}/*r*^{2}, and the strength of the gravitational force is *Gm*^{2}/*r*^{2}. Since both of these quantities have *r*^{2} in the denominator, you simply need to compare the numerical values of *kq*^{2} and *Gm ^{2}*. There's no contest. Since

*kq*^{2} = (9 × 10^{9} N·m^{2}/C^{2})(1 C)^{2} = 9 × 10^{9} N·m^{2}

and

*Gm*^{2} = (6.7 × 10^{-11} N·m^{2}/kg^{2})(1 kg)^{2} = 6.7 × 10^{-11} N·m^{2}

you can see that *kq*^{2} > *Gm*^{2}, so *F*_{E} is much stronger than *F*_{G}.