Question

The value of gravitational constant $G$ in Meter-Kilogram-Second system is $6.67\times {{10}^{-11}}\,N-{{m}^{2}}k{{g}^{-2}}$. What will be its value in the centimeter gram second system?
$\begin{align}
  & A.\,\,\,6.67\times {{10}^{-5}} \\
 & B.\,\,\,6.67\times {{10}^{-9}} \\
 & C.\,\,\,6.67\times {{10}^{-8}} \\
 & D.\,\,\,6.67\times {{10}^{-13}} \\
\end{align}$

Answer 1

Hint: This is a simple question of translating the unit system from one to another and determining the value after the translation. To do the unit translation, first understand the relation between the unit to be translated and the unit it should be translated to so that that value can be placed in place of the unit and get the final answer.

Complete Step-by-Step solution:
According to the question, we need to translate the Meter-Kilogram-Second system to Centimeter-Gram-Second system, which means meter needs to be translated to centimeter and kilogram to gram.
We know that,
$\begin{align}
  & 1\,m=100\,cm,\,\text{and} \\
 & 1\,kg=1000\,g \\
\end{align}$

Now, substituting these values in the value of gravitational constant, we get-
$\begin{align}
  & G=6.67\times {{10}^{-11}}\,N-{{m}^{2}}k{{g}^{-2}} \\
 & \Rightarrow G=6.67\times {{10}^{-11}}\,N-{{({{10}^{2}}\,cm)}^{2}}{{({{10}^{3}}\,g)}^{-2}} \\
 & \Rightarrow G=6.67\times {{10}^{-11}}\times {{10}^{4}}\times {{10}^{-6}}\,N-c{{m}^{2}}{{g}^{-2}} \\
 & \therefore G=6.67\times {{10}^{-13}}\,N-c{{m}^{2}}{{g}^{-2}} \\
\end{align}$

Therefore, the correct answer is Option (D).

Additional Information:
The gravitational constant, denoted by the letter $G$, is an empirical physical constant involved in the calculation of gravitational effects in Sir Isaac Newton's law of universal gravitation and in Albert Einstein's general theory of relativity.

In Newton's law, it is the proportionality constant connecting the gravitational force between two bodies with the product of their masses and the inverse square of their distance. In the Einstein field equations, it quantifies the relation between the geometry of spacetime and the energy–momentum tensor.

Note:
This type of question is rarely asked in papers as it is the simplest form of marks scoring question that anyone can get. Sometimes, people make mistakes in this type of questions as well when they overthink and the simplest error that is done is translating the unit which is not asked to translate in the question. Just remember the units and their value to get the answer for this question.