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Question: The velocity 'v' of a part cle at time t is given by,v =\(\frac{a}{t}\)+\(\frac{bt}{t^{2} + c}\). Th...

The velocity 'v' of a part cle at time t is given by,v =at\frac{a}{t}+btt2+c\frac{bt}{t^{2} + c}. The dimensions of a, b, c are respectively –

A

LT -2, L, T\text{LT}\text{ }^{\text{-2}}\text{, L, T}

B

L, L, T2\text{L, L, }\text{T}^{2}

C

L, LT, T -2\text{L, LT, T}\text{ }^{\text{-2}}

D

L, L, LT2\text{L, L, L}\text{T}^{2}

Answer

L, L, T2\text{L, L, }\text{T}^{2}

Explanation

Solution

[a] = [vt] = L

[b] = [vt] = L

[c] = [t2] = T2 \lbrack c\rbrack\ = \ \lbrack t^{2}\rbrack\ = \text{ }\text{T}^{2}\