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1.Units, Dimensions and Measurement
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ઊર્જા $U = \frac{{A\sqrt x }}{{{x^2} + B}},\,$ હોય,તો $AB$ નું પારિમાણીક સૂત્ર
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
