First slide

Dimensions of physical quantities

Question

The position of a particle at time r is given by the relation $x (t) = (\frac{v_{0}}{α}) (1 - e^{- α t}),$ where v₀ is a constant and $α$ > 0. I The dimensions of v₀ and a are respectively

Moderate

A

$M^{0} L^{1} T^{- 1} and T^{- 1}$
B

$M^{0} L^{1} T^{- 1} and L T^{- 2}$
C

$M^{0} L^{1} T^{- 1} and T$
D

$M^{0} L^{1} T^{- 1} and T$

Solution

$\begin{array}{l} Dimension of α t = [M^{0} L^{0} T^{0}] ∴ [α] = [T^{- 1}] \\ Again [\frac{v_{0}}{α}] = [L] so [v_{0}] = [L T^{- 1}] \end{array}$

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