JEE MAIN - Physics (2023 - 25th January Evening Shift - No. 13)
Match List I with List II
| List I | List II | ||
|---|---|---|---|
| A. | Young's Modulus (Y) | I. | $$\mathrm{[ML^{-1}T^{-1}]}$$ |
| B. | Co-efficient of Viscosity ($$\eta$$) | II. | $$\mathrm{[ML^2T^{-1}]}$$ |
| C. | Planck's Constant (h) | III. | $$\mathrm{[ML^{-1}T^{-2}]}$$ |
| D. | Work function ($$\varphi $$) | IV. | $$\mathrm{[ML^2T^{-2}]}$$ |
Choose the correct answer from the options given below :
A-II, B-III, C-IV, D-I
A-I, B-II, C-III, D-IV
A-I, B-III, C-IV, D-II
A-III, B-I, C-II, D-IV
Explanation
$$
\begin{aligned}
& \mathrm{Y}=\frac{\text { Stress }}{\text { Strain }}=\frac{\mathrm{F} / \mathrm{A}}{\Delta \ell / \ell}=\frac{\left[\mathrm{MLT}^{-2}\right]}{\left[\mathrm{L}^2\right]}=\left[\mathrm{ML}^{-1} \mathrm{~T}^{-2}\right] \\\\
& \mathrm{F}=6 \pi \eta \mathrm{rv} \Rightarrow \eta=\frac{\mathrm{F}}{6 \pi \mathrm{rv}} \\\\
& {[\eta]=\frac{\left[\mathrm{MLT}^{-2}\right]}{[\mathrm{L}]\left[\mathrm{LT}^{-1}\right]}=\left[\mathrm{ML}^{-1} \mathrm{~T}^{-1}\right]} \\\\
& \mathrm{E}=\mathrm{h} v \Rightarrow \mathrm{h}=\frac{\mathrm{E}}{v}=\frac{\left[\mathrm{ML}^2 \mathrm{~T}^{-2}\right]}{\left[\mathrm{T}^{-1}\right]}=\left[\mathrm{ML}^2 \mathrm{~T}^{-1}\right]
\end{aligned}
$$
Work function has same dimension as that of energy, so $[\phi]=\left[\mathrm{ML}^2 \mathrm{~T}^{-2}\right]$
Work function has same dimension as that of energy, so $[\phi]=\left[\mathrm{ML}^2 \mathrm{~T}^{-2}\right]$
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