First slide

Dimensions of physical quantities

Question

The velocity v of a particle at time t is given by the equation $v = at + \frac{b}{t + c}$ . The dimensions of a, b, c are respectively

Moderate

A

$L^{2}, T, {LT}^{2}$
B

${LT}^{2}, LT, L$
C

${LT}^{- 2}, L, T$
D

$L, LT, T^{2}$

Solution

$\begin{array}{l} [v] = [at] = [\frac{b}{t + c}] and [t] = [c] \\ \Rightarrow [c] = T \\ \Rightarrow [t + c] = T \\ \Rightarrow \frac{[b]}{T} = {LT}^{- 1} \\ \Rightarrow [b] = L and [a] = {LT}^{- 2} \\ ∴ [a] = {LT}^{- 2}, [b] = L, [c] = T . \end{array}$

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