If force (F), work (W) and Velocity (V) are taken as fundametal quantities then the dimensinal formula of Time (T) is:

W^{1} F^{1} V^{1}

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W^{1} F^{1} V^{- 1}

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W^{- 1} F^{- 1} V^{- 1}

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W^{1} F^{- 1} V^{- 1}

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Solution

The correct option is C $W^{1} F^{- 1} V^{- 1}$
$T = F^{α} W^{β} V^{γ}$
$M^{0} L^{0} T^{1} = (M^{1} L^{1} T^{- 2})^{α} (M^{1} L^{2} T^{- 2})^{β} (L T^{- 1})^{γ}$
$M^{0} L^{0} T^{1} = M^{α + β} L^{α + 2 β + γ} T^{- 2 α - 2 β - γ}$
$\Rightarrow α + β = 0$
$α + 2 β + γ = 0$
$- 2 α - 2 β - γ = 1$
$\Rightarrow α = - 1, β = 1, γ = - 1$
$\Rightarrow T = F^{- 1} W^{1} V^{- 1}$

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If force (F), work (W) and Velocity (V) are taken as fundametal quantities then the dimensinal formula of Time (T) is:

The correct option is C W1F−1V−1T=FαWβVγM0L0T1=(M1L1T−2)α(M1L2T−2)β(LT−1)γ M0L0T1=Mα+βLα+2β+γT−2α−2β−γ⇒α+β=0α+2β+γ=0−2α−2β−γ=1⇒α=−1,β=1,γ=−1⇒T=F−1W1V−1