Question

Why is the following situation impossible? The centers of two homogeneous spheres are 1.00 m apart. The spheres are each made of the same element from the periodic table. The gravitational force between the spheres is 1.00 N.

Short answer

The highest atomic mass in the periodic table is 294 u and the mass which we are getting by calculation is $m_1=1.22\times {10}^5\text{kg}$which is higher as compare to 294 u, hence not possible.

Step-by-step solution

Step 1: Newton’s Law

Newton’s law of universal gravitation states that the gravitational force of attraction between any two particles of masses ${\text{M}}_{\text{1}}{\text{andM}}_2$separated by a distance r has the magnitude:

$F_g=G\frac{m_1.m_2}{r^2}$

Where,$G=6.674\times {10}^{-11}\text{N}·{\text{m}}^{\text{2}}{\text{/kg}}^{\text{2}}$ is the universal gravitational constant. This equation enables us to calculate the force of attraction between masses under many circumstances.

Explain the reasoning

Wefindthereasonfortheabovequestionbyfindingthemassofsphere.

Given:

Gravitational force:$F_g=1\text{N}$

The distance between the centers of two spheres:$r=30\text{cm}=0.3\text{m,}$

According to Newton’s law of universal gravitation, we have

$$\begin{gathered} F_g=G\frac{m_1.m_2}{r^2} \\ 1=6.67\times {10}^{-11}\times \frac{m_1.m_1}{1^2}..............\left(\because m_1=m_2\right) \\ {m_1}^2=\frac{{10}^{11}}{6.67} \\ {m}_1={10}^5\sqrt{\frac{10}{6.67}}\text{kg} \\ {m}_1=1.22\times {10}^5\text{kg} \end{gathered}$$

But the highest atomic mass in the periodic table is 294 u, so this is impossible that the gravitational force between the spheres is 1.00 N.