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, c are respectively :-

Options

A. `[LT^(-2)],[L]` and `[T]`
B. `[L^(2)],[T]` and `[LT^(2)]`
C. `[LT^(2)],[LT]` and `[L]`
D. `[L],[LT]` and `[T^(2)]`

Answer

A

Explanation

The given expression is
`v = at +(b)/(t+c)`
From principle of homogeneity
`[a] [t] = [v]`
`[a] = ([v])/([t]) = ([LT^(-1)])/([T]) = [LT^(-2)]`