The velocity `v` of a particle is given in terms of time `t` by the equation
`v=at+(b)/(t+c)` The dimensions of `a,b` and `c` are :

Options

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

Answer

B

Explanation

`v=at+(b)/(t+c),` at has same dimensions as `v`
`:.at=LT^(-1)` or `a=LT^(-2)`
`c` has the same dimensions as `t. :.c=T`
Also `(b)/(t+c)`has the dimensionsof `v`
`:.b=vt=LT^(-1).T^(1)=L`
Thus `a,b,c` respectively are `LT^(2),L,T.`
Hence correct choice is `(b)`.