The velocity $v$ of a particle depends upon the time $t$ according to the equation $v = a + b t + \frac{c}{d + t}$ . What is the dimension of $c$ ?

c = [L]

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c = [T]

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c = [M]

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c = [M L]

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Solution

The correct option is D $c = [L]$
From the principal of homogeneity,
$[a] = [v] o r [a] = [L T^{- 1}]$
$[b t] = [v] o r [b] = \frac{[v]}{[t]} = \frac{[L T^{- 1}]}{[T]}$
or, $[b] = [L T^{- 2}]$
Similarly, $[d] = [t] = [T]$
Further, $\frac{[c]}{[d + t]} = [v] o r [c] = [v] [d + t]$
or, $[c] = [L T^{- 1}] [T] o r [c] = [L]$

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