Dimensional Formula of Kinetic Energy

The dimensional formula of Kinetic Energy is given by,

[M¹ L² T^-2]

Where,

• M = Mass
• L = Length
• T = Time

Derivation

Kinetic energy (K.E) = [Mass × Velocity²] × 2^-1 . . . . . (1)

The dimensional formula of Mass = [M¹ L⁰ T⁰] . . . . (2)

Since, Velocity = Distance × Time^-1 = [L] × [T]^-1

∴ The dimensional formula of velocity = [M⁰ L¹ T^-1] . . . . (3)

On substituting equation (2) and (3) in equation (1) we get,

⇒ Kinetic energy = [Mass × Velocity²] × 2^-1

Or, K.E = [M¹ L⁰ T⁰] × [M⁰ L¹ T^-1]² = [M¹ L² T^-2]

Therefore, Kinetic Energy is dimensionally represented as [M¹ L² T^-2].

⇒ Check Other Dimensional Formulas:

• Dimensions of Angular Velocity
• Dimensions of Modulus of Rigidity
• Dimensions of Energy Density
• Dimensions of Rotational Kinetic Energy
• Dimensions of Boltzmann Constant