Question

The value of the universal gravitational constant \(G=6.67\times10^{-11}\,Nm^{2}/kg^{2}\) in CGS system is-

• A. \(6.67\times10^{11}\)
• B. \(6.67\times10^{-18}\)
• C. \(6.67\times10^{-8}\)
• D. \(6.67\times10^{8}\)

Hint:

When converting physical constants between SI and CGS systems, separately convert force, length and mass units, then combine the powers of ten carefully.

Answer 1

The Correct Option is C

Step 1: Understand what is asked.
We are given the universal gravitational constant $G = 6.67 \times 10^{-11}\ Nm^2/kg^2$ in the SI system. We must rewrite the same value in the CGS system (using dyne, centimetre and gram).

Step 2: List the unit conversions.
In CGS units the basic conversions are $1\ N = 10^5\ dyne$, $1\ m = 100\ cm$ and $1\ kg = 1000\ g$. So $1\ m^2 = 10^4\ cm^2$ and $1\ kg^2 = 10^6\ g^2$.

Step 3: Put these into G.
The units of $G$ are $Nm^2/kg^2$, so we replace each part: $G = 6.67 \times 10^{-11} \times \dfrac{10^5 \times 10^4}{10^6}$.

Step 4: Simplify the powers of ten.
The top gives $10^5 \times 10^4 = 10^9$. Dividing by $10^6$ gives $10^9 / 10^6 = 10^3$. So the extra factor is $10^3$.

Step 5: Combine the numbers.
Now $G = 6.67 \times 10^{-11} \times 10^3 = 6.67 \times 10^{-8}$ in CGS units (dyne cm$^2$/g$^2$).

Step 6: Check the other options and conclude.
Positive powers like $10^{11}$ or $10^8$ would mean $G$ got bigger, which is wrong since the conversion factor is only $10^3$. The value $10^{-18}$ is far too small. So the correct CGS value is $6.67 \times 10^{-8}$.
\[ \boxed{\text{$6.67\times10^{-8}$}} \]