Question

check the correctness of the equation W=1/2mv^2-1/2mu^2 using the dimensional analysis where W is the work done ,m is the mass of body , u its initial velocity and mu is final velocity

Answer 1

Answer:

Writing the dimensions either side of the given equation.

$\longrightarrow \: \rm W = \dfrac{1}{2} mv^2 - \dfrac{1}{2} mu^2$

$\dag \: \rm LHS = W = work \: done = F\times s =[MLT^{-2}] [L] = \bf[ML^{2} T^{-2}]$

$\dag \: \rm RHS = \dfrac{1}{2} mv^2 = mass\times (velocity)^2 = [M] [LT^{-1}]^{2}=[M] [L^2T^{-2}]= \bf [ML^2T^{-2}]$

and ,

$\dag \: \rm RHS = \dfrac{1}{2} mu^2 = mass\times (velocity)^2 = [M] [LT^{-1}]^{2}=[M] [L^2T^{-2}]= \bf [ML^2T^{-2}]$

LHS = RHS.

As the dimensions of the both the sides are same. Therefore given formula is dimensionally correct.