Dimensions of physical quantities

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Question

In the given equation $y = A (1 - e^{- \frac{k t}{v}})$ ; t is time and v velocity. If dimensional formula of k is $M^{x} L^{y} T^{z}$ then value of $(x + 2 y + z)$ is equal to_________

Moderate

Solution

$\begin{array}{l} \frac{k t}{v} = dimensionless; \frac{k t}{v} = 1 \\ k = \frac{v}{t} \\ \Rightarrow k = \frac{[L^{1} T^{- 1}]}{[T^{1}]} = [L T^{- 2}] = [M^{0} L^{1} T^{- 2}] \\ S o, x = 0, y = 1, z = - 2 \\ Value of x + 2 y + z = 0 + 2 - 2 = 0 \end{array}$

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