The position x of a particle at time t is given by `x=(V_(0))/(a)(1-e^(-at))`, where `V_(0)` is constant and `a gt 0`. The dimensions of `V_(0)` and a are

Options

A. `[M^(0)LT^(-1)]` and `[M^(0)L^(0)T^(-1)]`
B. `[M^(0)LT^(0)]` and `[M^(0)LT^(-1)]`
C. `[M^(0)LT^(-1)]` and `[MLT^(-2)]`
D. `[M^(0)LT^(-1)]` and `[M^(0)LT]`

Answer

A

Explanation

As `a xx t` is dimensionless,
`:. [a] = (1)/([t])= (1)/([T])= [T^(-1)]= [M^(0)L^(0)T^(-1)]`
Also `[x]= ([V_(0)])/([a])` or `[V_(0)]= [x][a]= [L][M^(0)L^(0)T^(-1)] = [M^(0)LT^(-1)]`