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

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

b $[{x^2}]\, = [B]$ $[B] = [L^2]$ $\left[ U \right] = \frac{{[A]\,[{x^{1/2}}]}}{{[{x^2}]\, + \,[B]}}$ $⇒ [M{L^2}{T^{ - 2}}] = \frac{{[A]\,[{L^{1/2}}]}}{{[{L^2}]}}$ $\therefore\,[A] = [M{L^{7/2}}{T^{ - 2}}]$ $[AB]\, = \,[M{L^{7/2}}{T^{ - 2}}] \times [{L^2}]$ $ = [M{L^{11/2}}{T^{ - 2}}]$

SECTION - A [PHYSICS MCQ]

GSEB - English Medium

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

Medium

STD 11 Science
JEE
STD 11 - 1. units,dimensions and measurement
Physics

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