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1.Units, Dimensions and Measurement
hard
An expression of energy density is given by $u=\frac{\alpha}{\beta} \sin \left(\frac{\alpha x}{k t}\right)$, where $\alpha, \beta$ are constants, $x$ is displacement, $k$ is Boltzmann constant and $t$ is the temperature. The dimensions of $\beta$ will be.
A
$\left[ ML ^{2} T ^{-2} \theta^{-1}\right]$
B
$\left[ M ^{0} L ^{2} T ^{-2}\right]$
C
$\left[ M ^{0} L ^{0} T ^{0}\right]$
D
$\left[ M ^{0} L ^{2} T ^{0}\right]$
(JEE MAIN-2022)
Solution
$\frac{\alpha[ L ]}{\left[ ML ^{2} T ^{-2}\right]}=\left[ M ^{0} L ^{0} T ^{0}\right]$
$\alpha=\left[ ML ^{1} T ^{-2}\right]$
$\frac{\alpha}{\beta}=\frac{\left[ ML ^{2} T ^{-2}\right]}{\left[ L ^{3}\right]} \Rightarrow \beta=\frac{\left[ ML ^{1} T ^{-2}\right]\left[ L ^{3}\right]}{ ML ^{2} T ^{-2}}$
Standard 11
Physics
