Question

The gravitational force between two identical objects at a separation of 1 m is 0.0667 mg wt. The masses of the objects are:

($G=6.67\times {10}^{-11}N{m}^2/K{g}^2$ and $g=10m/s^2$)

• A. 200kg, 200kg
• B. 100kg, 100 kg
• C. 300kg, 300kg
• D. 400kg, 400kg

Answer 1

Answer: (B)

100kg, 100 kg

Given : $F=0.0667$ mg wt $=0.0667\times {10}^{-6}\times 10$ N , $r=1$ m
Using the expression: $F=\frac{Gmm}{r^2}$

Plugging in the values, we get:
$\Rightarrow F=\frac{(6.67\times {10}^{-11})\left(m^2\right)}{1^2}$
$\Rightarrow 0.0667\times {10}^{-5}=\frac{(6.67\times {10}^{-11})\left(m^2\right)}{1^2}$
$\Rightarrow 6.67\times {10}^{-7}=\frac{(6.67\times {10}^{-11})\left(m^2\right)}{1^2}$
$\Rightarrow m^2=\frac{6.67\times {10}^{-7}}{6.67\times {10}^{-11}}={10}^4$ kg

$\Rightarrow m=100kg$