Physical World Units And Measurements Ques 10
10. 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)
Show Answer
Answer:
Correct Answer: 10.(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}] $
BETA
