Question

Derived the formula for kinetic energy of a partical having mass m and velocity v using dimetional analysis

Answer 1

Answer:

K.E =1/2mv^2

Explanation:

Let a particle of mass m be moving with velocity v. suppose its kinetic energy is given by

K.E=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,

=>K.E=1/2MV^2

I HOPE IT HELPS