| 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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