Question

kinetic energy depends upon mass of body and velocity of body establish the relation

Answer 1

Answer:

Correction: Kinetic Energy depends both on mass and velocity of the body.

We know that Energy is denoted [ M¹ L²T⁻² ]

⇒ Kinetic Energy = k [ M ] ᵃ [ V ]ᵇ

Here, 'k' is a constant

⇒ [ V ] ᵇ = [ M⁰ L¹ T⁻¹ ] ᵇ

⇒ Kinetic Energy = k [ M ] ᵃ [ M⁰ L¹ T⁻¹ ] ᵇ

⇒ [ M¹ L²T⁻² ] = k [ M ] ᵃ [ L ] ᵇ [ T ] ⁻ᵇ

Comparing the equations on both sides we get,

⇒ M¹ = Mᵃ

⇒ a = 1

Similarly,

⇒ L² = Lᵇ

⇒  b = 2

⇒ T⁻² = T⁻ᵇ

⇒ b = 2

Hence the formula for Kinetic Energy is:

⇒ K.E. = k [ M ] ᵃ [ V ] ᵇ

⇒ K.E. = k [ M ] ¹ [ V ] ²

This is the dimensional formula of Kinetic Energy.

On experiments, we get to know that, value of k is 1/2.

Hence K.E. = 1/2 mv²

Explanation:

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