The position of a particle at time t is given by the equation `x(t) = V_(0)/A (1-e^(At))`
`V_(0)` = constant and A > 0
Dimensions of `V_(0)` and A respectively are

Options

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

Answer

D

Explanation

The dimensional formulae for `V_(0) is [M^(0)LT^(-1)]` and A is `[M^(0)L^(0)T^(-1)]`
Exponential function has no dimensions. `:. V_(0)/A = [M^(0)LT^(-1)]/[M^(0)L^(0)T^(-1)] = [L]`