Question

In the $CGS$ system of units, the magnitude of the force is $100\text{dyne}$. If in another system of units, the fundamental physical quantities like mass, length and time are expressed in kilogram, metre and minute respectively, the magnitude of the force in this system of units is

• A. $0.036$
• B. $0.36$
• C. $3.6$
• D. $36$

Answer 1

The correct option is C $3.6$

For any physical quantity,
Numerical value $\times$ Unit $=$ constant
$\Rightarrow n_2{u}_2=n_1{u}_1$
$\Rightarrow n_2\left[M_2{L}_2{T}_2^{-2}\right]=n_1\left[M_1{L}_1{T}_1^{-2}\right]$
$\Rightarrow n_2=n_1\left(\frac{M_1}{M_2}\right)\left(\frac{L_1}{L_2}\right){\left(\frac{T_1}{T_2}\right)}^{-2}$
$\Rightarrow n_2=100\left(\frac{\text{g}}{\text{kg}}\right)\left(\frac{\text{cm}}{\text{m}}\right){\left(\frac{\text{s}}{\text{min}}\right)}^{-2}$
$\Rightarrow n_2=100\times \left(\frac{1}{{10}^3}\right)\times \left(\frac{1}{100}\right)\times {\left(\frac{1}{60}\right)}^{-2}$
$\Rightarrow n_2=3.6$