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1.Units, Dimensions and Measurement
medium
Which two of the following five physical paramenters have the same dimensions $?$
$(1) $ energy density
$(2)$ refractive index
$(3) $ dielectric constant
$(4) $ Young's modulus
$(5)$ magnetic field
A$1$ and $4$
B$1$ and $5$
C$2$ and $4$
D$3$ and $5$
(AIPMT-2008)
Solution
Energy density = $[ {\frac{{workd\,done}}{{volume}}} ] = \frac{{ML{T^{ – 2}} \cdot L}}{{{L^3}}} = [ {M{L^{ – 1}}{T^{ – 2}}}$
Young's modulus = $\left[ Y \right] = \left[ {\frac{{Force}}{{Area}}} \right] \times \frac{{\left[ l \right]}}{{\left[ {\Delta l} \right]}}$
$= \frac{{ML{T^{ – 2}}}}{{{L^2}}}\, \cdot \frac{L}{L} = \left[ {M{L^{ – 1}}{T^{ – 2}}} \right]$
The dimensionsof $1$ and $4$ are the same.
Young's modulus = $\left[ Y \right] = \left[ {\frac{{Force}}{{Area}}} \right] \times \frac{{\left[ l \right]}}{{\left[ {\Delta l} \right]}}$
$= \frac{{ML{T^{ – 2}}}}{{{L^2}}}\, \cdot \frac{L}{L} = \left[ {M{L^{ – 1}}{T^{ – 2}}} \right]$
The dimensionsof $1$ and $4$ are the same.
Standard 11
Physics
