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Answer:
The dimension of the physical quantity α in the given equation is [L{-2}T2]1. This result can be obtained by analyzing the dimensions of the other quantities involved in the equation.
Given the equation: [ W = \frac{F}{\alpha \cdot v} ]
We can break down the dimensions of the quantities:
Force (F):
Dimensional formula of force: ([F] = \text{Mass} \cdot \text{Acceleration} = [M][LT^{-2}])
Velocity (v):
Dimensional formula of velocity: ([v] = [LT^{-1}])
Work (W):
Dimensional formula of work: ([W] = [ML2T{-2}])
Now let’s find the dimension of α: [ \alpha = \frac{F}{W \cdot v} ] [ [\alpha] = \frac{[F]}{[W][v]} = \frac{[MLT{-2}]}{[ML2T{-2}][LT{-1}]} = [L{-2}T2] ]
Hence, the dimension of α is [L{-2}T2].