Question

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

Answer 1

Answer:

the formula of kinetic energy is 1/2mv2

Answer 2

So, we have to derive the formula for kinetic energy of a particle having mass m and velocity v using dimensional analysis.

First of all, we know Kinetic energy of a body or particle depends on its velocity and mass.

We know the dimensional formula of Energy, so we have

⇒ [E] = k [m]ˣ [v]ʸ

Where,

• k is a constant and it is equal to 1/2

We know, Dimensional formula of

• Energy = [ML²T⁻²]
• Mass = [M]
• Velocity = [LT⁻¹]

So,

⇒ [ML²T⁻²] = [M]ˣ [LT⁻¹]ʸ

⇒ M¹ L² T⁻² = Mˣ Lʸ T⁻ʸ

Comparing each physical quantities, we get

⇒ M¹ = Mˣ

⇒ x = 1

Also,

⇒ L² = Lʸ

⇒ y = 2

Further,

⇒ T⁻² = T⁻ʸ

⇒ y = 2

We assumed the kinetic energy as,

⇒ E = k [m]ˣ [v]ʸ

Substituting values, we get

⇒ E = 1/2 × (m)¹ × (v)²

⇒ E = 1/2 mv²

So, The formula for kinetic energy is derived that is equal to 1/2 mv².