Question

The mass of the moon is 1% of the mass of the earth. The ratio of the gravitational pull of the earth on the moon and that of the moon on earth will be:

• A. $1:1$
• B. $1:10$
• C. $1:100$
• D. $2:1$

Answer 1

Answer: (A)

$1:1$

Given,

$m_1=m$

$m_2=0.01m$

$r=$ distance between moon and the earth

$G=$ gravitational constant

The gravitational pull of the earth on the moon

$F_{em}=\frac{G{m}_1{m}_2}{r^2}$

$F_{em}=G\frac{m\times 0.01m}{r^2}$ . . . . . . . .(1)

The gravitational pull of the moon on the earth,

$F_{me}=G\frac{m\times 0.01m}{r^2}$

ratio, $\frac{F_{em}}{F_{me}}=\frac{0.01G{m}^2/r^2}{0.01G{m}^2/r^2}=\frac{1}{1}$

$F_{em}:F_{me}=1:1$

The correct option is A.