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Question: The value of \(G\) for two bodies in vacuum is \(6.67 \times {10^{ - 11}}N{m^2}k{g^{ - 2}}\). Its va...

The value of GG for two bodies in vacuum is 6.67×10−11Nm2kg−26.67 \times {10^{ - 11}}N{m^2}k{g^{ - 2}}. Its value in a dense medium of density 1010gmcm3{10^{10}}gmc{m^3} will be:
A) 6.67×10−11Nm2kg−26.67 \times {10^{ - 11}}N{m^2}k{g^{ - 2}}
B) 6.67×10−31Nm2kg−26.67 \times {10^{ - 31}}N{m^2}k{g^{ - 2}}
C) 6.67×10−21Nm2kg−26.67 \times {10^{ - 21}}N{m^2}k{g^{ - 2}}
D) 6.67×10−10Nm2kg−26.67 \times {10^{ - 10}}N{m^2}k{g^{ - 2}}

Explanation

Solution

We can find the solution of the given question, if we know in detail about the gravitational constant. We need to know the values of gravitational constant if they are in different mediums. So, based on the concept of gravitational constant we can conclude with the solution of the given question.

Complete step by step answer:
We know that the gravitational force shows the relation between the masses of two bodies and the distance between them. Mathematically,
F=GmMR2F = \dfrac{{GmM}}{{{R^2}}}.
Here, GG is the Universal gravitational constant.
As, it can be seen that we say it as a universal gravitational constant, so it means that the value of gravitational constant will be the same everywhere.
So, we can conclude that the value of gravitational constant will be the same even if the medium is denser or rarer.

Hence, option (A), i.e. 6.67×10−11Nm2kg−26.67 \times {10^{ - 11}}N{m^2}k{g^{ - 2}} is the correct choice of the given question.

Note: One should not confuse the gravitational constant with acceleration due to gravity. We denote universal gravitational constant by GG and its value is 6.67×10−11Nm2kg−26.67 \times {10^{ - 11}}N{m^2}k{g^{ - 2}} whereas acceleration due to gravity is denoted by ggand its value is 9.8ms−29.8m{s^{ - 2}}. Universal gravitational constant was first introduced by Newton, so at some places we find it written as Newton’s law of universal gravitation. We use universal gravitational constant to find out the gravitational force exerted between two bodies. We find that the value of acceleration due to gravity changes on the surface of the earth from one place to another. But the value of the universal gravitational constant does not change.