Question

question #9
the two figures show two bodies of equal mass.
compared to the bodies in figure 1, the gravitational attraction between the bodies in figure 2 is
a one - half as strong.
b one - fourth as strong.
c twice as strong.
d four times as strong.

Explanation:

Step1: Write the formula for gravitational force

The formula for gravitational force is \( F = G\frac{m_1m_2}{r^2} \). Let the mass of each body be \( m \), so \( m_1 = m_2=m \). For Figure 1, \( r_1 = 1\space cm \), and for Figure 2, \( r_2 = 2\space cm \).

Step2: Calculate the ratio of forces

The force in Figure 1 is \( F_1=G\frac{m\times m}{r_1^2}=G\frac{m^{2}}{1^{2}} = Gm^{2} \).
The force in Figure 2 is \( F_2=G\frac{m\times m}{r_2^2}=G\frac{m^{2}}{2^{2}}=\frac{Gm^{2}}{4} \).
Now find the ratio \( \frac{F_2}{F_1}=\frac{\frac{Gm^{2}}{4}}{Gm^{2}}=\frac{1}{4} \).

Answer:

B. one - fourth as strong.