Question

If the units of force, energy and velocity are $10$ N, $100$ J and $5$ m/s then the unit of mass is :

• A. 1 kg
• B. 2 kg
• C. 3 kg
• D. 4 kg

Answer 1

The correct option is D 4 kg

$Force=\left[M^1{L}^1{T}^{-2}\right]=F$
$Energy=\left[M^1{L}^2{T}^{-2}\right]=E$
$Velocity=\left[L{T}^{-1}\right]=V$
$M^1\alpha F^a{E}^b{V}^c$
$M^{\prime }={\left(M^1{L}^1{T}^{-2}\right)}^a{\left(M^1{L}^2{T}^{-2}\right)}^b{\left(L{T}^{-1}\right)}^c$
$1=a+b:b+c=-1:c=-2$
$0=a+2b+c:-(2a+2b)-c=0:b=1$
$0=-2a-2b-c:a=0$
$\Rightarrow Mass=\frac{Energy}{{\left(Velocity\right)}^2}=\frac{100}{{\left(5\right)}^2}=4kg$