Question

In a particular system the units of length, mass, and time are chosen to be $10cm,100g$, and $0.1s$ respectively. The units of force in this system will be equal to?

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

Answer 1

The correct option is A

$1N$

Step 1: Given

Length $x=10cm$

$=0.1m$

Mass $m=100g$

$=0.1kg$

Time $t=0.1s$

Step 2: Calculate the force

If $a$ is the acceleration then the expression of force is given as

$F=ma$

Again acceleration $a=\frac{v}{t}$, where $v$ is the velocity.

Again velocity $v=\frac{x}{t}$where x is the displacement.

$\therefore F=m\frac{x}{t^2}$

Upon substituting these values we get,

$F=0.1\times \frac{0.1}{0.1\times 0.1}$

$=1N$

Hence, the correct answer is option (A).