If Energy is given by U = frac{{A√ x }}{{{x^2} + B}},, , then dimensions of AB is

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1.Units, Dimensions and Measurement

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if Energy is given by $U = \frac{{A\sqrt x }}{{{x^2} + B}},\,$, then dimensions of $AB$ is

A

$ML^{7/2}T^{ - 2}$

B

$M{L^{11/2}}{T^{ - 2}}$

C

${M^2}{L^{9/2}}{T^{ - 2}}$

D

$M{L^{13/2}}{T^{ - 3}}$

Solution

$[{x^2}]\, = [B]$ $[B] = [L^2]$

$\left[ U \right] = \frac{{[A]\,[{x^{1/2}}]}}{{[{x^2}]\, + \,[B]}}$

$⇒ [M{L^2}{T^{ – 2}}] = \frac{{[A]\,[{L^{1/2}}]}}{{[{L^2}]}}$

$\therefore\,[A] = [M{L^{7/2}}{T^{ – 2}}]$

$[AB]\, = \,[M{L^{7/2}}{T^{ – 2}}] \times [{L^2}]$ $ = [M{L^{11/2}}{T^{ – 2}}]$

Standard 11

Physics

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