Question

The position of a particle at time t is given by the relation x(t)= $\left(\frac{v_0}{\alpha }\right)(1-c^{-at})$ where $v_0$ and $\alpha$ are constants . The dimensions of $v_0$ and $\alpha$ are respectively

• A. M^oL¹T^-1 and T^-1
• B. M^oL¹T^o and T^-1
• C. M^oL¹T^-1 and LT^-2
• D. M^oL¹T^-1 and T

Answer 1

The correct option is A M^oL¹T^-1 and T^-1

Dimension of $\alpha$ t = $\left[M^0{L}^0{T}^0\right]\therefore \left[\alpha \right]=\left[T^{-1}\right]$
Again $\left[\frac{v_0}{\alpha }\right]$= [L] so $\left[v_0\right]=\left[L{T}^{-1}\right]$