Physical World Units and Measurements - Result Question 16
16. Which two of the following five physical parameters have the same dimensions? [2008]
(A) Energy density
(B) Refractive index
(C) Dielectric constant
(D) Young’s modulus
(E) Magnetic field
(a) (B) and (D)
(b) (C) and (E)
(c) (A) and (D)
(d) (A) and (E)
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Answer:
Correct Answer: 16. (c)
Solution:
- (c) Energy density $=\frac{\text{ Energy }}{\text{ Volume }}$
$\Rightarrow \frac{[ML^{2} T^{-2}]}{[L^{3}]}=[ML^{-1} T^{-2}]$
Refractive index and dielectric constant have no dimensions.
Young’s Modulus $=\frac{F}{A} \times \frac{l}{\Delta l}$
$\Rightarrow \frac{[MLT^{-2}]}{[L^{2}[.} \cdot \frac{[L]}{[L]}=[ML^{-1} T^{-2}]$.
Magnetic field, $B=\frac{F}{i \ell}=\frac{[MLT^{-2}]}{[A][L]}$
$ =[MT^{-2} A^{-1}] $
