Question

In C.G.S. system, the magnitude of a force is 100 dynes. In another system where the fundamental physical quantities are kilogram, metre and minute, the magnitude of the force is

• A. 0.036
• B. 0.36
• C. 3.6
• D. 36

Answer 1

The correct option is C 3.6

We know that the dimension of Force is $ML{T}^{-2}$,
Let the magnitude of force in the new system be $n_2$
$n_2=100{\left(\frac{M_1}{M_2}\right)}^1{\left(\frac{L_1}{L_2}\right)}^1{\left(\frac{T_1}{T_2}\right)}^{-2}$
$=100{\left(\frac{gm}{kg}\right)}^1{\left(\frac{cm}{m}\right)}^1{\left(\frac{sec}{min}\right)}^{-2}$
$=100{\left(\frac{gm}{{10}^{3}gm}\right)}^1{\left(\frac{cm}{{10}^{2}cm}\right)}^1{\left(\frac{sec}{60sec}\right)}^{-2}$
$n_2=100\times \frac{3600}{{10}^5}=3.6$