Chapter 13, Problem 27A

Calculate the force of gravity between a newborn baby of mass 4 kg and the obstetrician of mass 75 kg, who is 0.3 m from the baby. Which exerts more gravitational force on the baby, Mars or the obstetrician? By how much?

To determine

Force of gravity between a new-born baby and the obstetrician.

To identify: The object that will exert more force on the baby along with the amount of excessive force.

Answer to Problem 27A

The force of gravity between baby and the obstetrician $F_{12}=2.22\times {10}^{-7}\text{N}$ and the obstetrician exerts more force on the baby by 8.33 times.

Explanation of Solution

Given:

The mass of new-born baby is, $m_1=4\text{kg}$

The mass of the obstetrician is, $m_2=75\text{kg}$

Distance between new-born baby and obstetrician, $r_{12}=0.3\text{m}$

The mass of the planet mars is, $m_3=6.4\times {10}^{23}\text{kg}$

Mars position closest to Earth, $r_{13}=8\times {10}^{10}\text{m}$

Formula Used:

From Newton’s law of gravitation,

  $F=\frac{G{m}_1{m}_2}{r^2}$

  $F$ is force of gravity, $G$ is gravitational constant, $m_1$ and $m_2$ are mass of two objects and $r$ is distance between the two objects.

Calculation:

As gravitational constant $G=6.67\times {10}^{-11}{\text{N-m}}^2{\text{/kg}}^{\text{2}}$

On substituting the values in above relation, the force of gravity between new-born baby and the obstetrician,

  $\begin{array}{l}{F}_{12}=\frac{\left(6.67\times {10}^{-11}{\text{N-m}}^2{\text{/kg}}^{\text{2}}\right)\times \left(4\text{kg}\right)\times \left(75\text{kg}\right)}{{\left(0.3\text{m}\right)}^2}\\ =2.22\times {10}^{-7}\text{N}\end{array}$

And, the force of gravity between a new-born baby and the planet Mars, when Mars is closest to earth is

  $\begin{array}{l}{F}_{13}=\frac{\left(6.67\times {10}^{-11}{\text{N-m}}^2{\text{/kg}}^{\text{2}}\right)\times 4\times \left(6.4\times {10}^{23}\text{kg}\right)}{{\left(8\times {10}^{10}\text{m}\right)}^2}\\ =2.668\times {10}^{-8}\text{N}\end{array}$

Here, $F_{12}>F_{13}$

So, the obstetrician exerts more force on the baby by,

  $\frac{F_{12}}{F_{13}}=\frac{2.22\times {10}^{-7}\text{N}}{2.668\times {10}^{-8}\text{N}}=8.33\text{times}$

Conclusion:

Therefore, the force of gravity between a new-born baby and the obstetrician $F_{12}=2.22\times {10}^{-7}\text{N}$

The obstetrician exerts more force on the baby by 8.33 times.