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The physical quantity impulse is defined as the product of force and time. Which of the following physical quantities has the same dimensions as impulse?

  1. Linear momentumAnswer
  2. B
    Work done
  3. C
    Power
  4. D
    Force

Answer

Linear momentum
Linear momentum is calculated as mass times velocity, which yields the base dimensions [MLT−1][M L T^{-1}]. This is identical to impulse, which is force times time ([MLT−2]×[T]=[MLT−1][M L T^{-2}] \times [T] = [M L T^{-1}]).

Step-by-Step Solution

1
Determine the dimensions of impulse.
Impulse=Force×Time=[MLT−2][T]=[MLT−1]\text{Impulse} = \text{Force} \times \text{Time} = [M L T^{-2}][T] = [M L T^{-1}]
Force has base dimensions [MLT−2][M L T^{-2}] and time has dimension [T][T].
2
Determine the dimensions of linear momentum.
Linear Momentum=Mass×Velocity=[M][LT−1]=[MLT−1]\text{Linear Momentum} = \text{Mass} \times \text{Velocity} = [M][L T^{-1}] = [M L T^{-1}]
Mass has base dimension [M][M] and velocity has dimensions [LT−1][L T^{-1}].
3
Compare the dimensions of impulse and linear momentum.
Both quantities have identical dimensions of [MLT−1][M L T^{-1}].
By the impulse-momentum theorem, impulse equals change in momentum.

Key Concept

Dimensional analysis of physical quantities
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Topics

Physical Quantities, Units and Dimensions

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