Question

Derive the formula for kinetic energy of a partical 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

x = 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

Kinetic energy is one of the types of energy and it is defined as the energy in an object due to its virtue of motion. The dimension of kinetic energy will be the same as that of energy. Therefore, kinetic energy is measured in Joules (SI unit of energy) and its dimensional formula will be [M1L2T−2].