Force and pressure
Mass and power
Energy and velocity
Force and velocity
Answer is Right!
Answer is Wrong!
The correct answer is D. Force and velocity.
The dimensions of force are $MLT^{-2}$ and the dimensions of velocity are $LT^{-1}$. Therefore, the dimensions of force times velocity are $ML^{2}T^{-3}$.
The dimensions of mass are $M$, the dimensions of power are $ML^{2}T^{-3}$, and the dimensions of energy are $ML^{2}T^{-2}$. Therefore, none of the other options could be the product of two quantities with the correct dimensions.
Here is a more detailed explanation of each option:
- Option A: Force and pressure. The dimensions of force are $MLT^{-2}$ and the dimensions of pressure are $ML^{-1}T^{-2}$. Therefore, the dimensions of force times pressure are $ML^{2}T^{-4}$. This is not the correct answer because the dimensions of the product are not $M^{2}L^{2}T^{-3}$.
- Option B: Mass and power. The dimensions of mass are $M$ and the dimensions of power are $ML^{2}T^{-3}$. Therefore, the dimensions of mass times power are $ML^{3}T^{-3}$. This is not the correct answer because the dimensions of the product are not $M^{2}L^{2}T^{-3}$.
- Option C: Energy and velocity. The dimensions of energy are $ML^{2}T^{-2}$ and the dimensions of velocity are $LT^{-1}$. Therefore, the dimensions of energy times velocity are $ML^{3}T^{-3}$. This is not the correct answer because the dimensions of the product are not $M^{2}L^{2}T^{-3}$.
- Option D: Force and velocity. The dimensions of force are $MLT^{-2}$ and the dimensions of velocity are $LT^{-1}$. Therefore, the dimensions of force times velocity are $ML^{2}T^{-3}$. This is the correct answer because the dimensions of the product are $M^{2}L^{2}T^{-3}$.