JEE Mains · Physics · STD 11 - Units,dimensions and measurement
- JEE Mains 2023
- Medium
- MCQ
Match List \(I\) with List \(II\)
| List \(I\) | List \(II\) |
| \((A)\) Young's Modulus \((Y)\) | \((I)\) \(\left[ M L ^{-1} T ^{-1}\right]\) |
| \((B)\) Co-efficient of Viscosity \((\eta)\) | \((II)\) \(\left[ M L ^2 T ^{-1}\right]\) |
| \((C)\) Planck's Constant \((h)\) | \((III)\) \(\left[ M L ^{-1} T ^{-2}\right]\) |
| \((D)\) Work Function \((\phi)\) | \((IV)\) \(\left[ M L ^2 T ^{-2}\right]\) |
Pick an option to check your answer.
Answer & Solution
Correct Answer
(B) \((A)-(III), (B)-(I), (C)-(II), (D)-(IV)\)
Step-by-step Solution
Detailed explanation
\(Y =\frac{\text { Stress }}{\text { Strain }}=\frac{ F / A }{\Delta \ell / \ell}=\frac{\left[ MLT ^{-2}\right]}{\left[ L ^2\right]}=\left[ ML ^{-1} T ^{-2}\right]\)
\(F =6 \pi \eta rv \Rightarrow \eta=\frac{ F }{6 \pi rv }\)
\({[\eta]=\frac{\left[ MLT ^{-2}\right]}{[ L ]\left[ LT ^{-1}\right]}=\left[ ML ^{-1} T ^{-1}\right]}\)
\(E = h v \Rightarrow h =\frac{ E }{v}=\frac{\left[ ML ^2 T ^{-2}\right]}{\left[ T ^{-1}\right]}=\left[ ML ^2 T ^{-1}\right]\)
Work function has same dimension as that of energy, so \([\phi]=\left[ ML ^2 T ^{-2}\right]\)
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