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Units and Measurements question

2022 · 27 Jul · Shift 2 · Q41
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Units and Measurements question

2022 · 27 Jul · Shift 2 · Q41

JEE MainPhysicsUnits and MeasurementsMCQ+4 / −1
An expression of energy density is given by u=αβsin⁡(αxkt)u=\frac{\alpha}{\beta} \sin \left(\frac{\alpha x}{k t}\right)u=βα​sin(ktαx​), where α,β\alpha, \betaα,β are constants, xxx is displacement, kkk is Boltzmann constant and t is the temperature. The dimensions of β\betaβ will be :
  1. A
    [ML2 T−2θ−1]\left[\mathrm{ML}^{2} \mathrm{~T}^{-2} \theta^{-1}\right][ML2 T−2θ−1]
  2. B
    [M0 L2 T−2]\left[\mathrm{M}^{0} \mathrm{~L}^{2} \mathrm{~T}^{-2}\right][M0 L2 T−2]
  3. C
    [M0 L0 T0]\left[\mathrm{M}^{0} \mathrm{~L}^{0} \mathrm{~T}^{0}\right][M0 L0 T0]
  4. D
    [M0 L2 T0]\left[\mathrm{M}^{0} \mathrm{~L}^{2} \mathrm{~T}^{0}\right][M0 L2 T0]
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