Question

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

Answer 1

Hii Dear,

◆ Answer -

KE = 1/2 mv²

● Explanation -

Let a particle of mass m be moving with velocity v. Suppose it's kinetic energy ia given by -

KE = k.m^x.v^y

In dimensional form,

[KE] = [m]^x.[v]^y

[L2M1T-2] = [M1]^x.[L1T-1]^y

[L2M1T-2] = [L^y.M^x.T^-y]

Comparing indexes,

y = 2

y = 2x = 1

Putting this in our previous equation -

KE = k.m^1.v^2

Value of k can be experimentally determined as 1/2,

KE = 1/2 mv²

Thanks dear...

Answer 2

Answer:

$\frac{1}{2}mv^2$

Explanation:

We are given that a particle of mass m and velocity v

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

Let kinetic energy of particle =$Km^x v^y$

We know that dimension of mass = M

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

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

Substitute both values of kinetic energy equal then we get

$Km^xv^y=[M][L^2T^{-1}]=[M^1][(LT^{-1})^2]$

Comparing on both sides then we get

x=1 and y=2

Then , Kinetic energy=$Kmv^22$

We know that formula of kinetic energy

K.E=$\frac{1}{2}mv^2$

k is constant and dimension of constant value is zero .

Substitute K=$\frac{1}{2}$

Then , the formula of kinetic energy=$\frac{1}{2}mv^2$