Question

Which of the following physical quantities has the same dimensions as \( \dfrac{\text{Force} \times \text{Time}}{\text{Mass}} \)?

• A. Velocity
• B. Acceleration
• C. Momentum
• D. Impulse

Hint:

Always simplify dimensional expressions step-by-step. Cancel out common units (like mass here) and compare the final dimensional formula with standard quantities like velocity \( (L T^{-1}) \), acceleration \( (L T^{-2}) \), etc.

Answer 1

The Correct Option is A

Step 1: Write down the dimensional formula for Force.
\[ \text{Force} = \text{mass} \times \text{acceleration} = M \cdot L \cdot T^{-2} \] Step 2: Multiply Force with Time and divide by Mass. \[ \frac{\text{Force} \times \text{Time}}{\text{Mass}} = \frac{M \cdot L \cdot T^{-2} \cdot T}{M} = \frac{M \cdot L \cdot T^{-1}}{M} = L \cdot T^{-1} \] Step 3: Recognize the dimensional formula.
\[ L \cdot T^{-1} \quad \text{is the dimensional formula for Velocity} \] Therefore, the correct answer is Velocity.