# The velocity v of a particle at time t is given by v = at+b/t+c,where a, b and c are constants. The dimensions of a, b and c are

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The velocity v of a particle at time t is given by v =  at+b/t+c,where a, b and c are constants. The dimensions of a, b and c are

(a) [L],[LT] and [LT-2]

(b) [LT-2], [L] and [T]

(c) [L2], [T] and [LT-2]

(d) [LT-2], [LT] and [L]

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Answer: (b) [LT-2], [L] and [T]

According to the principle of dimensional homogeneity

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

Dimension of a =$\frac{\mathrm{[v]}}{[t]}=\frac{LT_2}{T}=[LT^{-2}]$

Dimension of b =[v][t]=[LT-1T]=[L]

Dimension of c = [t]=[T]

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Correct Option  (b) [LT-2], [L] and [T]

Explanation:

v = at+ b/t+c

As c is added to t,

:. [c] = [T]