Question

Derive the formula for kinetic energy of particle having mass m and velocity v using dimensional analysis

Answer 1

Answer:

K. E =1/2MV²

Explanation:

W.=F*S

W=MV²/2S*S

W=1/2MV²

Answer 2

Answer:

Kinetic energy=$\frac{1}{2}mv^2$

Explanation:

We are given that

Mas of particle=m

Velocity of particle=v

We have to derive the dimensional formula for kinetic energy of particle using dimensional analysis

We know that dimension of mass=[M]

Dimension of velocity=$[LT^{-1}]$

Dimension of kinetic energy =$[M(LT^{-1})^2]$

Dimension of kinetic energy=$[ML^2T^{-2}]$

Kinetic energy=$kmv^2$

We know that dimension of kinetic energy =$[ML^2T^{-2}]$

Constant , k=$\frac{1}{2}$

Substitute the value then , we get

Hence, Kinetic energy=$\frac{1}{2}mv^2$