A) Plancks constant and angular momentum
B) Impulse and linear momentum
C) Moment of inertia and moment of a force
D) Energy and torque
Correct Answer: C
Solution :
[a] Planck s constant \[=\frac{\text{Energy}}{\text{Frequency}}=\frac{[M{{L}^{2}}-{{T}^{-2}}]}{[{{T}^{-1}}]}\] Frequency \[[M{{L}^{2}}{{T}^{-1}}]\] Angular momentum = Moment of inertia \[\times \]Angular velocity \[=[M{{L}^{2}}]\times [{{T}^{-1}}]=[M{{L}^{2}}{{T}^{-1}}]\] [b] Impulse = Force \[\times \] Time \[=[ML{{T}^{-2}}][T]=[ML{{T}^{-1}}]\] and linear momentum = Mass \[\times \] Velocity \[=[M][L{{T}^{-1}}]=[ML{{T}^{-1}}]\] [c] Moment of inertia \[\text{=}\,\text{Mass}\,\text{ }\!\!\times\!\!\text{ (Distance}{{\text{)}}^{\text{2}}}\] \[\text{ }\!\![\!\!\text{ M}{{\text{L}}^{2}}\text{ }\!\!]\!\!\text{ }\]and moment of force = Force \[\times \] Distance \[=[ML{{T}^{-2}}][L]=[M{{L}^{2}}{{T}^{-2}}]\] [d] Energy \[=[M{{L}^{2}}{{T}^{-2}}]\] and torque \[=[M{{L}^{2}}{{T}^{-2}}]\] So, [c] option has different dimensions.
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