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Which of the following physical quantities have the same dimensions

  • A.Momentum and impulse
  • B.Power and young modulus
  • C.Energy and angular momentum
  • D.Force constant and moment of inertia

Answer: A

Momentum and impulse share dimensions.

Impulse is force times time and momentum is mass times velocity: \[[\mathrm{Ft}] = \mathrm{MLT^{-2}\cdot T} = \mathrm{MLT^{-1}},\qquad [\mathrm{mv}] = \mathrm{M\cdot LT^{-1}} = \mathrm{MLT^{-1}}\] They must agree, since the impulse–momentum theorem says one equals the change in the other.

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