Which two of the following five physical parameters have the same dimensions? (1) energy density (2)…

Which two of the following five physical parameters have the same dimensions? (1) energy density (2) refractive index (3) dielectric constant (4) Young's modulus (5) magnetic field
  1. 2 and 4
  2. 3 and 5
  3. 1 and 4
  4. 1 and 5

Solution

(1) Energy density,
$\begin{aligned}
& =\frac{\text { Energy }}{\text { Volume }} \\
& =\frac{\left[\mathrm{ML}^2 \mathrm{~T}^{-2}\right]}{\left[\mathrm{L}^3\right]}=\left[\mathrm{ML}^{-1} \mathrm{~T}^{-2}\right]
\end{aligned}$
(2) Refractive index hole no dimensions.
(3) Dielectric constant has no dimensions.
(4) Young's modulus,
$Y=\frac{F l}{A \Delta l}=\frac{\left[\mathrm{MLT}^{-2}\right][\mathrm{L}]}{\left[\mathrm{L}^2\right][\mathrm{L}]}=\left[\mathrm{ML}^{-1} \mathrm{~T}^{-2}\right]$
(5) Magnetic field,
$B=\frac{F}{I l}=\frac{\left[\mathrm{MLT}^{-2}\right]}{[\mathrm{A}][\mathrm{L}]}=\left[\mathrm{MT}^{-2} \mathrm{~A}^{-1}\right]$
Therefore, option (c) is correct.

Asked in: NEET 2008 (Screening)

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