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1.Units, Dimensions and Measurement
medium
$E,\,m,\,l$ and $G$ denote energy, mass, angular momentum and gravitational constant respectively, then the dimension of $\frac{{E{l^2}}}{{{m^5}{G^2}}}$ are
AAngle
BLength
CMass
DTime
(AIIMS-1985)
Solution
(a) $[E] = [M{L^2}{T^{ – 2}}],\;[m] = [M],\;[l] = [M{L^2}{T^{ – 1}}]$and $[G] = [{M^{ – 1}}{L^3}{T^{ – 2}}]$ Substituting the dimension of above quantities in the given formula :
$\frac{{E{l^2}}}{{{m^5}{G^2}}}$$\frac{{[M{L^2}{T^{ – 2}}]\,{{[M{L^2}{T^{ – 1}}]}^2}}}{{[{M^5}]\,{{[{M^{ – 1}}{L^3}{T^{ – 2}}]}^2}}} = \frac{{{M^3}{L^6}{T^{ – 4}}}}{{{M^3}{L^6}{T^{ – 4}}}} = [{M^0}{L^0}{T^0}]$
$\frac{{E{l^2}}}{{{m^5}{G^2}}}$$\frac{{[M{L^2}{T^{ – 2}}]\,{{[M{L^2}{T^{ – 1}}]}^2}}}{{[{M^5}]\,{{[{M^{ – 1}}{L^3}{T^{ – 2}}]}^2}}} = \frac{{{M^3}{L^6}{T^{ – 4}}}}{{{M^3}{L^6}{T^{ – 4}}}} = [{M^0}{L^0}{T^0}]$
Standard 11
Physics
