Question

If force, time and velocity are treated as fundamental quantities, then dimensional formula of energy will be

A. [FTV]
B. [FT²V]
C. [FTV²]
D. [FT²V²]

Answer 1

The dimensional formula of energy when force, time, and velocity are treated as fundamental quantities is [FTV].

Step-by-step explanation:

When force, time, and velocity are treated as fundamental quantities, the dimensional formula of energy can be determined by analyzing the dimensions of each term in the equation for energy. In this case, the equation for energy is E = FTV, where E is energy, F is force, T is time, and V is velocity.

Breaking down the dimensions of each term: [F] = MLT^-2 (force has dimensions of mass multiplied by length divided by time squared), [T] = T (time has dimensions of just time), and [V] = LT^-1 (velocity has dimensions of length divided by time).

By substituting these dimensions into the equation for energy, we get [E] = [F] * [T] * [V] = (MLT^-2) * T * (LT^-1) = M * L^2 * T^-2 * L * T^-1 = M * (LT^-2) * (LT^-1) = M * L^2 * T^-3. Therefore, the dimensional formula of energy is [FTV] or option A.