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Physics · UNITS AND MEASUREMENT
हिन्दीThe force \( F \) acting on an object as a function of position \( x \) and time \( t \) is given by \( F = A \sqrt{x} + B t^2 + C \ln(D x) \). The dimensional formula of \( \frac{A \cdot B}{D} \) is:
Correct answer · Option 3
\( [\text{M}^2 \text{L}^{7/2} \text{T}^{-4}] \)
Explanation
The argument of logarithm \( [Dx] = [1] \implies [D] = [\text{L}^{-1}] \).
\( [A\sqrt{x}] = [F] \implies [A] = [\text{M L}^{1/2} \text{T}^{-2}] \).
\( [Bt^2] = [F] \implies [B] = [\text{M L T}^{-4}] \).\nTherefore, \( [\frac{AB}{D}] = \frac{[\text{M L}^{1/2} \text{T}^{-2}][\text{M L T}^{-4}]}{[\text{L}^{-1}]} = [\text{M}^2 \text{L}^{7/2} \text{T}^{-4}] \).
