Question

When one metre, one $kg$ and one minute are taken as fundamental units, the magnitude of a force is 36 units. What is the value of this force on CGS system?

• A. $10^3$ dyne
• B. $10^5$ dyne
• C. $10^6$ dyne
• D. $10^7$ dyne

Answer 1

Answer: (A)

$M_1=1kg$
$L_1=1m$
$T_1=1min$
$n_1=36$
$M_2=1g$
$L_2=1cm$
$T_2=1s$
$n_2=?$
The dimensional formula of force is $\left[ML{T}^{-2}\right]$.
$\therefore a=1,b=1,c=-2$
$n_2=n_1{\left[\frac{M_1}{M_2}\right]}^a{\left[\frac{L_1}{L_2}\right]}^b{\left[\frac{T_1}{T_2}\right]}^c$
$=36{\left[\frac{1kg}{1g}\right]}^1{\left[\frac{1m}{1cm}\right]}^1{\left[\frac{1min}{1s}\right]}^{-2}$
$=36{\left[\frac{1000g}{g}\right]}^1{\left[\frac{100cm}{1cm}\right]}^1{\left[\frac{60s}{1s}\right]}^{-2}$
$=\frac{36\times 10^3\times 10^2}{3600}=10^3$
Hence, in the CGS system of units the value of given force is $10^3$ dyne.