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Physics · UNITS AND MEASUREMENT
हिन्दीAccording to the principle of homogeneity of dimensions, if the velocity \( v \) of a particle depends on time \( t \) as \( v = a t + \frac{b}{t + c} \), where \( a \), \( b \), and \( c \) are constants, then the dimensions of \( a \), \( b \), and \( c \) are respectively:
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Correct answer · Option A
\( [\text{L T}^{-2}], [\text{L}], [\text{T}] \)
Explanation
From principle of homogeneity: \( [c] = [t] = [T] \). Then \( [\frac{b}{t+c}] = [v] = [L T^{-1}] \implies [b] = [L T^{-1}][T] = [L] \). Similarly, \( [at] = [v] = [L T^{-1}] \implies [a] = [L T^{-2}] \).
