Question

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

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

Answer 1

Answer: (A)

$M_{1} =10 g$
$L_{1} =10 cm$
$T_{1} =0.1 s$
$n_{1} =1$
$M_{2}=1 kg$
$L_{2}=1 m$
$T_{2}=1 s$
$n_{2}=?$
The dimensional formula of force is $\left[ MLT ^{-2}\right]$.
$\therefore \quad a=1, b=1, c=-2$
$n_{2}=n_{1}\left(\frac{M_{1}}{M_{2}}\right)^{a}\left(\frac{L_{1}}{L_{2}}\right)^{b}\left(\frac{T_{1}}{T_{2}}\right)^{c}$
$=1\left(\frac{10 g }{1 kg }\right)^{1}\left(\frac{10 cm }{1 m }\right)^{1}\left(\frac{0.1 s }{1 s }\right)^{-2}$
$=1\left(\frac{10^{-2} kg }{1 kg }\right)^{1}\left(\frac{10^{-1} m }{1 m }\right)^{1}\left(\frac{0.1 s }{1 s }\right)^{-2}$
$=\frac{1 \times 10^{-2} \times 10^{-1}}{10^{-2}}$
$=10^{-1}=0.1$
Hence, the unit of force in a given system will be equivalent to $0.1 N$.