JEE Mains · Physics · STD 11 - Units,dimensions and measurement
- JEE Mains 2021
- Hard
- MCQ
In a typical combustion engine the work done by a gas molecule is given \(W =\alpha^{2} \beta e ^{\frac{-\beta x ^{2}}{ KT }}\), where \(x\) is the displacement, \(k\) is the Boltzmann constant and \(T\) is the temperature. If \(\alpha\) and \(\beta\) are constants, dimensions of \(\alpha\) will be
Pick an option to check your answer.
Answer & Solution
Correct Answer
(B) \(\left[ M ^{0} LT ^{0}\right]\)
Step-by-step Solution
Detailed explanation
\(kT\) has dimension of energy
\(\frac{\beta x ^{2}}{ kT }\) is dimensionless
\([\beta]\left[ L ^{2}\right]=\left[ ML ^{2} T ^{-2}\right]\)
\([\beta]=\left[ MT ^{-2}\right]\)
\(\alpha^{2} \beta\) has dimensions of work
\(\left[\alpha^{2}\right]\left[ MT ^{-2}\right]=\left[ ML ^{2} T ^{-2}\right]\)
\([\alpha]=\left[ M ^{0} LT ^{0}\right]\)
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