The dimensional formula of kinetic energy can be derived by analyzing its components. Kinetic energy (KE) is defined as the energy possessed by an object due to its motion. It depends on two factors: mass (M) and velocity (V). The dimensional formula for kinetic energy can be obtained as follows:
Kinetic energy (KE) = 1/2 * mass * velocity^2
Breaking it down further:
Mass (M) has the dimensional formula of [M]. Velocity (V) has the dimensional formula of [L][T]^-1 (length per unit time).
Substituting these values into the equation for kinetic energy:
KE = 1/2 * [M] * ([L][T]^-1)^2 = 1/2 * [M] * [L]^2 * [T]^-2
Simplifying further:
KE = [M] * [L]^2 * [T]^-2
Therefore, the dimensional formula for kinetic energy (KE) is [M] * [L]^2 * [T]^-2, where [M] represents mass, [L] represents length, and [T] represents time.