Dimensional formula for Kinetic Energy

Kinetic Energy is the energy possessed by a moving object. The dimensional formula for Kinetic Energy can be derived by using the formula for Kinetic Energy and taking into account the dimensions of the fundamental quantities involved.

Formula for Kinetic Energy

The formula for Kinetic Energy is:

Kinetic Energy = 1/2 * mass * (velocity)^2

Dimensions of Fundamental Quantities

The dimensions of the fundamental quantities involved are:

- Velocity (p) = [L][T]^-1
- Acceleration (q) = [L][T]^-2
- Density (r) = [M][L]^-3

Deriving the Dimensional Formula

Substituting the dimensions of the fundamental quantities in the formula for Kinetic Energy, we get:

Kinetic Energy = 1/2 * [M] * [L]^2 [T]^-2

Simplifying the above equation, we get:

Kinetic Energy = [M] [L]^2 [T]^-2

Therefore, the dimensional formula for Kinetic Energy is [M] [L]^2 [T]^-2.

Explanation

- The formula for Kinetic Energy involves the fundamental quantities of mass, velocity, and time.
- The dimensions of mass, velocity, and time are [M], [L][T]^-1, and [T], respectively.
- By substituting the dimensions of the fundamental quantities in the formula for Kinetic Energy, we get the dimensional formula for Kinetic Energy as [M] [L]^2 [T]^-2.
- This means that Kinetic Energy is directly proportional to the square of the velocity and the mass of the object.
- The dimensional formula helps in understanding the physical nature of the quantity and in making calculations involving Kinetic Energy.

KE=ML^2T^-2
p=LT^-1
q=LT^-2
r=ML^-3
Here comparing these three equiations
r=1
p+q=2
p=-q+2
-p-2q-3=-2
-p-2q=1
q-2-2q=1
-q=3
p=5
q=-3
dimensional formula of KE=p^5q^-3r^1