The velocity v of a particle at time A is given by `v = at+ (b)/(l +c)` where a ,b and c are constant The dimensions of a,b and 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

According to principal of homogenetly of dimensions the dimensions of theterms in a physical expression should be the same
The given expression is `v = dt + (b)/(1 + c)`
From principal of homogenetly
`[a] [t] = [v]`
`[a] = ([v])/([r]) = ([LT^(-1)])/([T]) = [LT^(-1)]`
similarly , `[c] = [r] = [T]`
Further, `([b])/([t +c]) = [v]`
or `[b] = [v] [t+ c]` or `[b] = [LT^(-1)][T^(-1)] [T] = [L]`