Question

A body of mass \( m = 3.513 \, \text{kg} \) is moving along the X-axis with a speed of \( 5.00 \, \text{ms}^{-1} \). The magnitude of its momentum is recorded as:

• A. \( 17.6 \, \text{kg ms}^{-1} \)
• B. \( 17.565 \, \text{kg ms}^{-1} \)
• C. \( 17.56 \, \text{kg ms}^{-1} \)
• D. \( 17.57 \, \text{kg ms}^{-1} \)

Hint:

Key points to remember:
- Momentum \( p = mv \) is a vector quantity
- In calculations, always consider significant figures
- The result should have same significant figures as the least precise measurement
- Here, 5.00 (3 sig figs) limits the precision of the answer

Answer 1

The Correct Option is B

Step 1: Calculate momentum
Momentum \( p \) is given by: \[ p = m \times v = 3.513 \, \text{kg} \times 5.00 \, \text{ms}^{-1} = 17.565 \, \text{kg ms}^{-1} \]
Step 2: Apply significant figures rules
The mass has 4 significant figures (3.513) and velocity has 3 (5.00). The result should be reported with the least number of significant figures in the input, which is 3.
Step 3: Verify options
Option (b) matches our correctly rounded result. The other options either show too many significant figures or incorrect rounding.