The velocity of a freely falling body in a resisting medium at any time 't' is given by $v = \frac{A}{B [1 - e^{B t}]} .$ The dimensions of 'A' are:

L

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{L T}^{- 2}

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{L T}^{- 1}

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L T

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Solution

The correct option is A ${L T}^{- 2}$
$V = \frac{A}{B (1 - e^{+ B t})}$
$\Rightarrow B t$ should be dimensionless.
$\Rightarrow B = T^{- 1}$
$\Rightarrow A = V T^{- 1} = [L T^{- 1} \times T^{- 1}]$
$\Rightarrow A = [L T^{- 2}]$

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