Question

Which of the following quantity represents the dimensions of momentum?

• A. Impulse
• B. Pressure
• C. Viscosity
• D. Power

Hint:

Impulse = Force × Time = Change in Momentum. Hence, both have the same dimensional formula.

Answer 1

The Correct Option is A

Momentum has dimensions: \[ \text{Momentum} = mv \Rightarrow [M][LT^{-1}] = [MLT^{-1}] \] Now consider the dimensions of each option: - Impulse = Force × Time \ \[ [F \cdot t] = [MLT^{-2}] \cdot [T] = [MLT^{-1}] \] Matches momentum - Pressure = Force / Area \ \[ [MLT^{-2}] / [L^2] = [ML^{-1}T^{-2}] \] - Viscosity = Stress / Rate of strain \ \[ [ML^{-1}T^{-2}] / [T^{-1}] = [ML^{-1}T^{-1}] \] - Power = Work / Time \ \[ [ML^2T^{-2}] / [T] = [ML^2T^{-3}] \] Only Impulse has the same dimensions as Momentum.