Question:
A body of mass \(0.4\) kg performs simple harmonic motion. It experiences a restoring force of \(0.4\) N when its displacement from the mean position is 4 cm. The force constant and magnitude of acceleration respectively are
A body of mass \(0.4\) kg performs simple harmonic motion. It experiences a restoring force of \(0.4\) N when its displacement from the mean position is 4 cm. The force constant and magnitude of acceleration respectively are
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k = F / x and a = F / m.
Updated On: Oct 1, 2026
- \(5 \text{N/}_{\text{m}},0.5 \text{m/}_{\text{s}^2}\)
- \(10 \text{N/}_{\text{m}},1 \text{m/}_{\text{s}^2}\)
- \(15 \text{N/}_{\text{m}},1.5 \text{m/}_{\text{s}^2}\)
- \(20 \text{N/}_{\text{m}},2 \text{m/}_{\text{s}^2}\)
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The Correct Option is B
Solution and Explanation
Step 1: Understanding the Concept
The restoring force in SHM is \(F = kx\), so \(k = F/x\). The acceleration is \(a = F/m\).
Step 2: Compute
\[ k = \frac{0.4}{0.04} = 10 \text{ N/m} \]
\[ a = \frac{0.4}{0.4} = 1 \text{ m/s}^2 \]
The displacement 4 cm must first be converted to 0.04 m; leaving it as 4 gives k = 0.1, which is not an option.
Final Answer:
The force constant is 10 N/m and the acceleration is 1 m/s\(^2\), option (B). \[ \boxed{10 \text{ N/m},\ 1 \text{ m/s}^2} \]
The restoring force in SHM is \(F = kx\), so \(k = F/x\). The acceleration is \(a = F/m\).
Step 2: Compute
\[ k = \frac{0.4}{0.04} = 10 \text{ N/m} \]
\[ a = \frac{0.4}{0.4} = 1 \text{ m/s}^2 \]
The displacement 4 cm must first be converted to 0.04 m; leaving it as 4 gives k = 0.1, which is not an option.
Final Answer:
The force constant is 10 N/m and the acceleration is 1 m/s\(^2\), option (B). \[ \boxed{10 \text{ N/m},\ 1 \text{ m/s}^2} \]
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