Question

K.E of an object depends upon mass of the object and velocity of the object. find the formula of K.E using dimensional analysis​

Answer 1

Since we  know that,

The dimension of energy [E]=[M1L2T−2]

The dimension of mass   [M]=[M1L0T0]

Dimension of velocity[V]=[M0L1T−1]

Let [E]=k[M]x[V]y

Where k is the proportionality constant which is a dimensionless quantity.

Therefore,

[M1L2T−2]=k[M1L0T0]x[M0L1T−1]y

So, x=1,y=2

Thus, We have

E=kmv2

It is found that k=21

Hence, E=21mv2

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