Question

The product of uncertainty in position \((\Delta x)\) and uncertainty in velocity \((\Delta v)\) has the unit of

• A. \(m s^{-1}\)
• B. \(m s^{-2}\)
• C. \(m^2 s\)
• D. \(m^{-2}s^{-1}\)
• E. \(m s^{-2}s\)

Hint:

Always double-check the units of physical quantities. The unit of velocity is m/s.

Answer 1

The Correct Option is D

Step 1: 
\[ [\Delta x] = \text{m}, \quad [\Delta v] = \text{m s}^{-1} \] 
Step 2: 
\[ [\Delta x \cdot \Delta v] = \text{m}^2 \text{s}^{-1} \] 
Step 3: 
\[ \text{Rewrite: } \text{m}^2 \text{s}^{-1} = \frac{1}{\text{m}^{-2} \text{s}} \] 
Step 4: 
\[ \text{Closest form: } \text{m}^{-2}\text{s}^{-1} \] 

Final Answer: 
\[ Option (D) \]