Question

In a particular system, the units 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 equal to

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

Answer 1

Answer: (A)

$1$ newton $= 1kg\, m/s^2$
$1 \,kg = 10^3g$ and $1\,m = 10^2\, cm$
so $1N=\frac{\left(10^{3}\,g\right)\left(10^{2}\,cm\right)}{s^{2}}$
$1N=\frac{100\times\left(10\,g\right)\times10\left(10\,cm\right)}{100\times\left(0.1\,s^{2}\right)}=10\times\frac{\left(10^{3}\,g\right)\left(10^{2}\,cm\right)}{\left(0.1\,s\right)^{2}}$
$1N = 10\times$ New unit of force
$\therefore $ New unit of force $=\frac{1}{10}N=0.1N$