Question

If force (F), work (W) and velocity (v) are taken as fundamental quantities. What is
the dimensional formula of time (T)?
(a) [WFv] (b) [WFv-1] (c) [W-1F -1v] (d) [WF-1v -1]​

Answer 1

Answer:

[WF−1V−1]

Explanation:

work done =force × distance

as distance = velocity ×time

since v= distance ÷ time

W = F.v.t

t= W÷Fv

(t)=[WF−1V−1]

Answer 2

If force (F), work (W) and velocity (v) are taken as fundamental quantities, the dimensional formula of time (T) is WF⁻¹v⁻¹.

• Work is the product of the force applied and the displacement of the body. It is given by the formula,

       $W = F * d$

• Force is the product of the mass of the body and the acceleration produced by it. It is given by the formula,

       $F = m * a$

• Acceleration is the change in velocity with respect to time. It is given by the formula,

        $a = \frac{v}{T}$

• Velocity is the change in position of the body with respect to time. It is given by the formula,

        $v = \frac{d}{T}$

        $d = v * T$

• Rewriting the work formula,

        $W = F * v * T$

• On rearranging, the dimensional formula of time (T) is,

        $T = \frac{W}{F * v}$