Question

# The velocity $$v$$ of a particle at time $$t$$ is given by $$v = at + \frac{b} {t + c}$$, where $$a, b\ and\ c$$ are constants.The dimensions of $$a, b\ and\ c$$ are respectively:

A
LT2, L and T
B
L2, T and LT2
C
LT2, LT and L
D
L, LT and T2

Solution

## The correct option is A LT$$^{-2}$$, L and TTwo terms can be added or subtracted if their dimensions are same.Thus $$c$$ has the dimension of time i.e.  $$[T]$$Dimension of $$v$$ and $$at$$ must be same.Thus dimensions of $$[a] = \dfrac{[v]}{[t]} = \dfrac{[LT^{-1}]}{[T]} = [LT^{-2}]$$Dimensions  $$[b] = [v][t] = [LT^{-1}][T] = L$$Physics

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