The dimensional formula of kinetic energy (K.E.) is obtained by dimensional analysis, which is a method of finding the dimensions of physical quantities using the dimensions of other quantities that are related to them. The dimensional formula of kinetic energy can be obtained as follows:
derivation
First, we know that the kinetic energy of an object is given by the formula:
K.E. = (1/2) * m * v^2
where m is the mass of the object and v is its velocity.
Next, we use the following dimensional formulas for mass (M), length (L), and time (T):
M = [m]
L = [l]
T = [t]
The velocity of an object can be defined as the distance covered by the object per unit time, so its dimensional formula is given by:
v = L/T = [l]/[t]
Squaring the velocity, we get:
v^2 = (L/T)^2 = L^2/T^2 = [l^2]/[t^2]
Finally, substituting the dimensional formulas of mass and velocity into the formula for kinetic energy, we get:
K.E. = (1/2) * m * v^2 = (1/2) * M * (L^2/T^2) = [M L^2]/[T^2]
So, the dimensional formula for kinetic energy is [M L^2]/[T^2].