Which two of the following five physical parameters have the same dimensions? [AIPMT (S) 2008] |
(1) energy density |
(2) refractive index |
(3) dielectric constant |
(4) Young's modulus |
(5) magnetic field |
A) 2 and 4
B) 3 and 5
C) 1 and 4
D) 1 and 5
Correct Answer: C
Solution :
(1) Energy density\[\text{=}\frac{\text{Energy}}{\text{Volume}}\] |
\[\text{=}\frac{[M{{L}^{2}}{{T}^{-2}}]}{[{{L}^{3}}]}=[M{{L}^{-1}}{{T}^{-2}}]\] |
(2) Refractive index hole no dimensions. |
(3) Dielectric constant has no dimensions. |
(4) Young's modulus, |
\[Y=\frac{Fl}{A\Delta l}=\frac{[ML{{T}^{-2}}]}{[{{L}^{2}}][L]}=[M{{L}^{-1}}{{T}^{-2}}]\] |
(5) Magnetic field, |
\[B=\frac{F}{Il}=\frac{[ML{{T}^{-2}}]}{[A][L]}=[M{{T}^{-2}}{{A}^{-1}}]\] |
Therefore, option [c] is correct. |
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