Question

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

Answer 1

Answer:

KE = 1/2mv²

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