Question

In a particular system, the unit of length, mass and time are chosen to be $10cm,10g$ and 0.1 s respectively. The unit of force in this system will be equivalent to

• A. $0.1N$
• B. $1N$
• C. $10N$
• D. $100N$

Answer 1

Answer: (A)

$M_1=10g$
$L_1=10cm$
$T_1=0.1s$
$n_1=1$
$M_2=1kg$
$L_2=1m$
$T_2=1s$
$n_2=?$
The dimensional formula of force is $\left[ML{T}^{-2}\right]$.
$\therefore a=1,b=1,c=-2$
$n_2=n_1{\left(\frac{M_1}{M_2}\right)}^a{\left(\frac{L_1}{L_2}\right)}^b{\left(\frac{T_1}{T_2}\right)}^c$
$=1{\left(\frac{10g}{1kg}\right)}^1{\left(\frac{10cm}{1m}\right)}^1{\left(\frac{0.1s}{1s}\right)}^{-2}$
$=1{\left(\frac{10^{-2}kg}{1kg}\right)}^1{\left(\frac{10^{-1}m}{1m}\right)}^1{\left(\frac{0.1s}{1s}\right)}^{-2}$
$=\frac{1\times 10^{-2}\times 10^{-1}}{10^{-2}}$
$=10^{-1}=0.1$
Hence, the unit of force in a given system will be equivalent to $0.1N$.