Question:
A particle is executing linear S.H.M. starting from mean position. The ratio of the kinetic energy to the potential energy of the particle at a point of half the amplitude is
A particle is executing linear S.H.M. starting from mean position. The ratio of the kinetic energy to the potential energy of the particle at a point of half the amplitude is
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Kinetic energy is proportional to A squared minus x squared, potential energy to x squared.
Updated On: Nov 13, 2026
- \(2:1\)
- \(3:1\)
- \(4:1\)
- \(8:1\)
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The Correct Option is B
Solution and Explanation
Step 1: Understanding the Concept
In S.H.M. \(KE=\dfrac12k(A^2-x^2)\) and \(PE=\dfrac12kx^2\).
Step 2: Substitute
At \(x=\dfrac A2\): \(KE\propto A^2-\dfrac{A^2}{4}=\dfrac{3A^2}{4}\) and \(PE\propto\dfrac{A^2}{4}\).
Step 3: Ratio
\(\dfrac{KE}{PE}=\dfrac{3A^2/4}{A^2/4}=3\), so the ratio is \(3:1\).
Final Answer:
The ratio of kinetic to potential energy is 3 : 1. \[ \boxed{\text{(B) }3:1} \]
In S.H.M. \(KE=\dfrac12k(A^2-x^2)\) and \(PE=\dfrac12kx^2\).
Step 2: Substitute
At \(x=\dfrac A2\): \(KE\propto A^2-\dfrac{A^2}{4}=\dfrac{3A^2}{4}\) and \(PE\propto\dfrac{A^2}{4}\).
Step 3: Ratio
\(\dfrac{KE}{PE}=\dfrac{3A^2/4}{A^2/4}=3\), so the ratio is \(3:1\).
Final Answer:
The ratio of kinetic to potential energy is 3 : 1. \[ \boxed{\text{(B) }3:1} \]
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