Question

The gravitational force acting on a particle of 1 g due to a similar particle is equal to 6.67 × 10−17 N. Calculate the separation between the particles.

Answer 1

The separation between the particles is, 1 m.

Explanation:

Step 1:

Given data in question  :

                  Here, the mass of $m_1$  and $m_2$ is ,

                  Mass = m₁ = m₂ = 1 g = 0.001 kg                  

We know ,    

                 $\mathrm{G}=6.67 \times 10^{-11} \mathrm{Nm}^{2} / \mathrm{kg}^{2}$

                 $\mathrm{F}_{\mathrm{g}}=6.67 \times 10^{-17}(\mathrm{given})$

Step 2:

Already we know the formula of gravitational,    

                   $F_{g}=\frac{G m_{1} m_{2}}{r^{2}}$

Putting the whole value into the formula given ,

                  $6.67 \times 10^{-17}=\frac{6.67 \times 10^{-11} \times 0.001 \times 0.001}{r^{2}}$

          $r^{2} \times 6.67 \times 10^{-17}=6.67 \times 10^{-11} \times 0.001 \times 0.001$

                                  $r^{2}=\frac{6.67 \times 10^{-11} \times 0.001 \times 0.001}{6.67 \times 10^{-17}}$

                                   $r^{2}=\frac{6.67 \times 10^{-11} \times 1 \times 10^{-6}}{6.67 \times 10^{-17}}$

                                   $r^{2}=\frac{6.67 \times 10^{-17}}{6.67 \times 10^{-17}}$

                                    $r^{2}=1$                      

                                     $r=\sqrt{1}$

                                      r = 1

Thus, the split between the two particles is therefore 1 m.