Question

A body of mass(m) moves with velocity (v) and acquire energy (E) given by E=1/2mv use dimensions to check weather the equation is homogeneous or not

Answer 1

Dimensional Analysis:

E = ½ m × v.

In order to check whether this equation is correct or not, we will dimensionally analyse the LHS and RHS of the equation.

LHS:

$\bigg[E\bigg] =\bigg[ M{L}^{2} {T}^{ - 2} \bigg]$

RHS:

$\bigg[ \dfrac{1}{2} mv\bigg] =\bigg[ M \times L {T}^{ - 1} \bigg]$

$\implies\bigg[ \dfrac{1}{2} mv\bigg] =\bigg[ M L {T}^{ - 1} \bigg]$

So, we can say:

$\boxed{LHS \: \neq \: RHS}$

So, equation is dimensionally incorrect !