If force (F), work (W) and velocity (V) are taken as fundamental quantities then the dimensional 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 D $[W^{1} F^{- 1} V^{- 1}]$
We know,

$[W] = M L^{2} T^{- 2}$

$[F] = M L T^{- 2}$

$[V] = L T^{- 1}$

Let,
$W^{a} F^{b} V^{c} = M^{0} L^{0} T$

$a + b = 0$

$2 a + b + c = 0$ , $a + c = 0$

$- 2 a - 2 b - c = 1$

$c = - 1, a = 1, b = - 1$

Hence , $[T] = [W F^{- 1} V^{- 1}]$

Option $D$ is the correct answer

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If force (F), work (W) and velocity (V) are taken as fundamental quantities then the dimensional formula of time (T) is

The correct option is D [W1F−1V−1]We know,[W]=ML2T−2[F]=MLT−2[V]=LT−1Let,WaFbVc=M0L0Ta+b=02a+b+c=0, a+c=0−2a−2b−c=1c=−1,a=1,b=−1Hence , [T]=[WF−1V−1]Option D is the correct answer