Question

Force acting on a particle is $10\text{N}$. If units of length and time are doubled and the unit of mass is halved then find the numerical value of force in the new system of units.

• A. $2.5$
• B. $3.5$
• C. $4.5$
• D. $5.5$

Answer 1

The correct option is A $2.5$

Given:
force $\left(f\right)=10\text{N}=10\text{kg}\frac{\text{m}}{{\text{s}}^2}$

If units of length and time are doubled and unit of mass is halved, then value of force in new system of units will be

$f=10\times \left[\frac{\frac{1}{2}\times 2}{(2{)}^2}\right]\text{unit}$

$\Rightarrow f=2.5\text{unit}$

$\begin{array}{c}\text{Why this question ?}\\ \text{Concept - In different system of units, the magnitude}\\ \text{and unit of measurement of physical quantities changes but}\\ \text{it's nature remain the same i.e. Force remain the force}\\ \text{Trick - We can also use}{n}_1{u}_1=n_2{u}_2,\text{where n is}\\ \text{numerical value and}u\text{is unit.}\end{array}$