The position of a particle at time `t` is given by the relation `x(t) = ( v_(0) /( alpha)) ( 1 - c^(-at))`, where `v_(0)` is a constant and `alpha gt 0`. Find the dimensions of `v_(0) and alpha`.

Options

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

Answer

a

Explanation

Dimension of `alpha t = [M^(0)L^(0)T^(0)] :. [a] = [T^(-1)]`
Again `[(v_(0))/(alpha)] rArr [a] = [P] xx [V^(2)] = [ML^(-1)T^(-2)][L^(6)]`
`= [ML^(5)T^(-2)]`