Question

The value of gravitation constant is $G=6.67\times {10}^{-11}N-m^2/k{g}^2$ in SI units. Convert it into CGS system of units.

• A. Thus, value of G in CGS system of units is $6.67\times {10}^{-8}dynec{m}^2/g^2.$
• B. Thus, value of G in CGS system of units is $6.67\times {10}^{-9}dynec{m}^2/g^2.$
• C. Thus, value of G in CGS system of units is $6.67\times {10}^{-7}dynec{m}^2/g^2.$
• D. Thus, value of G in CGS system of units is $6.67\times {10}^{-10}dynec{m}^2/g^2.$

Answer 1

Answer: (A)

Thus, value of G in CGS system of units is $6.67\times {10}^{-8}dynec{m}^2/g^2.$

Dimensional formula for G is $\left[M^{-1}{L}^3{T}^{-2}\right]$

Now, $n_1\left[M_1^{-1}{L}_1^3{T}_1^{-2}\right]=n_2\left[M_2^{-1}{L}_2^3{T}_2^{-2}\right]$

$n_2=n_1{\left[\frac{M_1}{M_2}\right]}^{-1}{\left[\frac{L_1}{L_2}\right]}^3{\left[\frac{T_1}{T_2}\right]}^{-2}$

Here, $n_1=6.67\times {10}^{-11}$

$M_1=1kg,M_2=1g={10}^{-3}kg,L_1=1m,L_2=1cm={10}^{-2}m,T_1=T_2=1s$

Substituting in above equation we get,
$n_2=6.67\times {10}^{-11}{\left[\frac{1kg}{{10}^{-3}kg}\right]}^{-1}{\left[\frac{1m}{{10}^{-2}m}\right]}^3{\left[\frac{1s}{1s}\right]}^{-2}$

or, $n_2=6.67\times {10}^{-8}$

Thus, value of G in CGS units is $6.67\times {10}^{-8}dyne{cm}^2/g^2.$