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

Answer

B

Explanation

Same dimensions can be added
This given formula is dimensionally valid
`v= at+(b)/(t+c)`
`at to v` (velocity)
`a[T] to [LT^(-1)]`
`implies a to [LT^(-2)]`
Again, `(b)/(t+c) to v`
But, `t+c=` time `=[T] implies c= [T]`
`(b)/([T])= [LT^(-1)]`
`b= [L]`