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The velocity v (in cm/sec) of a particle is given in terms of time (in sec) by the equation $v = at + \frac{b}{t + c}$ . The dimensions of a, b & c

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$a - L^{- 2}, b - T, c - {LT}^{2}$

$a - {LT}^{2}, b - LT, c - T$

$a - {LT}^{- 2}, b - L, c - T$

$a - L b - LT C - T^{2}$

answer is C.

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Detailed Solution

$v = at + \frac{b}{t + c}$

$Since t and c are added, \Rightarrow [c] = [t] = T^{1}$

$again, \frac{[b]}{[t] + [c]} = [v]$

$\Rightarrow \frac{[b]}{T} = {LT}^{- 1} \Rightarrow [b] = {TLT}^{- 1} = L^{1}$

$again, [a] [t] = [v]$

$\Rightarrow [a] = \frac{L^{1} T^{- 1}}{T^{1}} = L^{1} T^{- 2}$

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