Q128 / 180 · COMEDK 2021 · Physics
Which of the following quantity represents the dimensions of momentum?
- Correct answerAImpulse
- BPressure
- CViscosity
- DPower
Solution
The dimension of momentum $p$ is given by $p = mv$, where $m$ is mass ($M$) and $v$ is velocity ($LT^{-1}$). Thus, the dimensions of momentum are $[MLT^{-1}]$.
Impulse $J$ is defined as the change in momentum, $J = \Delta p = F \Delta t$. The dimensions of force $F$ are $[MLT^{-2}]$ and time $\Delta t$ is $[T]$. Therefore, the dimensions of impulse are $[MLT^{-2}] \times [T] = [MLT^{-1}]$.
Pressure is force per unit area, $[MLT^{-2}] / [L^2] = [ML^{-1}T^{-2}]$.
Viscosity (coefficient of viscosity) has dimensions $[ML^{-1}T^{-1}]$.
Power is work per unit time, $[ML^2T^{-2}] / [T] = [ML^2T^{-3}]$.
Comparing these, impulse has the same dimensions as momentum.
Answer: Impulse
Impulse $J$ is defined as the change in momentum, $J = \Delta p = F \Delta t$. The dimensions of force $F$ are $[MLT^{-2}]$ and time $\Delta t$ is $[T]$. Therefore, the dimensions of impulse are $[MLT^{-2}] \times [T] = [MLT^{-1}]$.
Pressure is force per unit area, $[MLT^{-2}] / [L^2] = [ML^{-1}T^{-2}]$.
Viscosity (coefficient of viscosity) has dimensions $[ML^{-1}T^{-1}]$.
Power is work per unit time, $[ML^2T^{-2}] / [T] = [ML^2T^{-3}]$.
Comparing these, impulse has the same dimensions as momentum.
Answer: Impulse
Hence, the correct answer is option: 'A'.