Question

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

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

Answer 1

Answer: (A)

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