Which of the following is not measured in units of energy?

Which of the following is not measured in units of energy?
  1. Couple \(\times\) angle turned through
  2. Moment of inertia \(\times\) (angular velocity) \(^{2}\)
  3. Force \(\times\) distance
  4. Impulse \(\times\) time

Solution

$\text { Energy }=M^{1} L^{2} T^{-2}$ Couple $\times$ (angle turned through) $=\overrightarrow{\mathrm{r}} \times \overrightarrow{\mathrm{f}} \times \theta=\left(\mathrm{L}^{1}\right)\left(\mathrm{M}^{1} \mathrm{~L}^{1} \mathrm{~T}^{-2}\right)\left(\mathrm{M}^{\circ} \mathrm{L}^{\circ} \mathrm{T}^{0}\right)=$ $\mathrm{M}^{1} \mathrm{~L}^{2} \mathrm{~T}^{-2}$ (Moment of Inertia) $\times$ (Angular velocity) $^{2}=\left(\mathrm{MR}^{2}\right) \times\left(\omega^{2}\right)=$ $\left(\mathrm{M}^{1}\right)\left(\mathrm{L}^{2}\right)\left(\mathrm{T}^{-2}\right)=\mathrm{M}^{1} \mathrm{~L}^{2} \mathrm{~T}^{-2}$ Force $\times$ distance $=\mathrm{M}^{1} \mathrm{~L}^{1} \mathrm{~T}^{-2} \times \mathrm{L}^{1}=\mathrm{ML}^{2} \mathrm{~T}^{-2}$ Impulse $\times$ time $=(\mathrm{f} \times \mathrm{t}) \times \mathrm{t}=\mathrm{M}^{1} \mathrm{~L}^{1} \mathrm{~T}^{-2} \times \mathrm{T} \times \mathrm{T}=\mathrm{M}^{1} \mathrm{~L}^{1} \rightarrow$ not a unit of energy

Asked in: JEE Mains - Units and Dimensions - Chapter Test

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