Question

A spring balance has a scale that reads 0 to 50 kg. The length of the scale is 20 cm. A body suspended from this spring, when displaced and released, oscillates with a period of 0.60 s. What is the weight of the body?

• A. 22.36 N
• B. 45 N
• C. 219.13 N
• D. 223.6 N

Hint:

Be careful not to confuse mass (kg) with weight (N).

Answer 1

The Correct Option is C

Step 1: Concept
First find the spring constant ($k = F/x$), then use the time period formula $T = 2\pi\sqrt{m/k}$.
Step 2: Analysis
$k = \frac{50 \times 9.8}{0.20} = 2450$ N/m. Time period $T = 0.60$ s.
Step 3: Calculation
$0.60 = 2\pi\sqrt{m/2450} \Rightarrow m = \frac{(0.60)^{2} \times 2450}{4\pi^{2}} \approx 22.36$ kg. Weight $W = mg = 22.36 \times 9.8 \approx 219.13$ N.
Step 4: Conclusion
Hence, the weight is approximately 219.13 N.
Final Answer:(C)