Question

If in a system, the force of attraction between two point masses of \[1{\rm{ kg}}\] each situated \[1{\rm{ km}}\] apart is taken as a unit of force and is called notwen (Newton written in reverse order) and if
\[G = 6.67 \times {10^{ - 11}}{\rm{ N - mk}}{{\rm{g}}^{ - 2}}\] in SI units then which of the following is true?

A. \[1 {\rm{ notwen}} = 6.67 \times {10^{ - 11}}{\rm{ newton}}\]
B. \[1 {\rm{ newton}} = 6.67 \times {10^{ - 17}}{\rm{ notwen}}\]
C. \[1 {\rm{ notwen }} = 6.67 \times {10^{ - 17}}{\rm{ newton}}\]
D. \[1 {rm{ notwen }} = 6.67 \times {10^{ - 12}}{\rm{ newton}}\]

Answer 1

Hint: We will use the concept of the gravitational law which says that the force of attraction between two given point masses is linearly proportional to the product of these masses and inversely proportional to the distance between them. We will remove the constant proportionality sign by adding a constant, which is called a constant of gravitation.

Complete step by step answer:
Given:
The mass of two point masses is \[m = 1{\rm{ kg}}\].
The distance between the masses is \[r = 1{\rm{ km}} \times \left( {\dfrac{{1000{\rm{ m}}}}{{{\rm{km}}}}} \right) = 1000{\rm{ m}}\].
The gravitational constant is \[G = 6.67 \times {10^{ - 11}}{\rm{ N - mk}}{{\rm{g}}^{ - 2}}\].

Let us write the expression for force of attraction between two point masses as below:
\[F = \dfrac{{G{m^2}}}{{{r^2}}}\]
Here F is the force of attraction between two given point masses.

We will substitute \[1{\rm{ kg}}\] for m, \[1000{\rm{ m}}\] for r and \[6.67 \times {10^{ - 11}}{\rm{ N - mk}}{{\rm{g}}^{ - 2}}\] for G in the above expression.
\[\begin{array}{c}
F = \dfrac{{\left( {6.67 \times {{10}^{ - 11}}{\rm{ N - }}{{\rm{m}}^2}{\rm{k}}{{\rm{g}}^{ - 2}}} \right){{\left( {1{\rm{ kg}}} \right)}^2}}}{{{{\left( {1000{\rm{ m}}} \right)}^2}}}\\
 = 6.67 \times {10^{ - 17}}{\rm{ newton }}
\end{array}\]

It is given that this force of attraction is called notwen so we can write:
\[1 {\rm{ notwen }} = 6.67 \times {10^{ - 17}}{\rm{ newton}}\]

Therefore, the force of attraction between the two-point masses is \[6.67 \times {10^{ - 17}}{\rm{ newton}}\], and option (C) is correct.

Additional information: The value of the gravitational constant is calculated experimentally by balancing the torsional force and its value the same for different conditions; therefore, it is termed as a constant value. We can replace the newton into its base units that are kilogram, metre and second to find the unit of gravitational constant in the KGS system.

Note:We can note that this force of attraction exists between every two bodies present in this universe which are separated by some distance. Lesser the distance higher the value of the force of attraction and higher the distance lesser will be the force of attraction.