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

Concept: The universal gravitational constant \(G\) appears in Newton's law of gravitation: \[ F=\frac{Gm_1m_2}{r^2} \] The value of \(G\) depends upon the system of units used. Here, \(G\) is given in SI units: \[ G=6.67\times10^{-11}\;Nm^2/kg^2 \] We have to convert it into CGS units.

Step 1: Write the required conversion factors. \[ 1N=10^5\;dyne \] \[ 1m=100cm \] Therefore, \[ 1m^2=10^4cm^2 \] Also, \[ 1kg=10^3g \] Hence, \[ 1kg^2=10^6g^2 \]

Step 2: Convert \(G\) into CGS units. \[ G_{CGS} = 6.67\times10^{-11} \times \frac{10^5\times10^4}{10^6} \] \[ = 6.67\times10^{-11}\times10^3 \] \[ = 6.67\times10^{-8} \] Therefore, \[ G=6.67\times10^{-8} \;dyne\cdot cm^2/g^2 \]