Question 116: Units , Dimensions and Error Analysis

Question

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 :

Accepted Answer

$$
\begin{aligned}
& \mathrm{Y}=\frac{	ext { Stress }}{	ext { Strain }}=\frac{\mathrm{F} / \mathrm{A}}{\Delta \ell / \ell}=\frac{\left[\mathrm{MLT}^{-2}ight]}{\left[\mathrm{L}^2ight]}=\left[\mathrm{ML}^{-1} \mathrm{~T}^{-2}ight] \\
& \mathrm{F}=6 \pi \eta \mathrm{rv} \Rightarrow \eta=\frac{\mathrm{F}}{6 \pi \mathrm{rv}} \\
& {[\eta]=\frac{\left[\mathrm{MLT}^{-2}ight]}{[\mathrm{L}]\left[\mathrm{LT}^{-1}ight]}=\left[\mathrm{ML}^{-1} \mathrm{~T}^{-1}ight]} \\
& \mathrm{E}=\mathrm{h} v \Rightarrow \mathrm{h}=\frac{\mathrm{E}}{v}=\frac{\left[\mathrm{ML}^2 \mathrm{~T}^{-2}ight]}{\left[\mathrm{T}^{-1}ight]}=\left[\mathrm{ML}^2 \mathrm{~T}^{-1}ight]
\end{aligned}
$$
Work function has same dimension as that of energy, so $[\phi]=\left[\mathrm{ML}^2 \mathrm{~T}^{-2}ight]$

Answer

A-II, B-III, C-IV, D-I

Answer

A-I, B-II, C-III, D-IV

Answer

A-I, B-III, C-IV, D-II

Answer

A-III, B-I, C-II, D-IV

Units , Dimensions and Error Analysis

Choose the correct answer: