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Derive an expression of kinetic energy of a body of mass 'm' and moving with velocity 'v', using dimensional analysis.

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student-name Vaishali Deshmukh asked in Physics

Derive an expression of kinetic energy of a body of mass 'm' and moving with velotiy 'v' ,using dimensional analysis.

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student-name Somnath Mazumder answered this

20158 helpful votes in Physics, Class XII-Science

We know, dimension of energy is, [E] = [M1L2T-2]

Dimension of mass is [m] = [M1L0T0]

Dimension of velocity is [v] = [M0L1T--1]

Suppose,

[E] = k [m]x [v]y

‘k’ is a proportionality constant which is a dimensionless quantity.

Therefore,

[M1L2T-2] = [M1L0T0]x [M0L1T--1]y

=> [M1L2T-2] = [MxLyT-y]

Thus, x = 1, y = 2

So, we have, E = k mv2

It is found that, k = ½

So, E = ½ mv2

Derived.