Question

If the length of the oscillating simple pendulum is made $\frac{1}{3}$ times the original keeping amplitude same then increase in its total energy at a place will be}

• A. 3 times
• B. 2 times
• C. 9 times
• D. 5 times

Hint:

"Increase in" refers to $\Delta E$, while "becomes" refers to the final value $E'$.

Answer 1

The Correct Option is B

Step 1: Concept
Total energy of a simple pendulum is $E = \frac{1}{2} m \omega^2 A^2$.

Step 2: Meaning
Since $\omega^2 = g/L$, the energy $E \propto 1/L$ when mass and amplitude are constant.

Step 3: Analysis
If $L' = L/3$, then $E' = 3E$. The increase in energy is $\Delta E = E' - E = 3E - E = 2E$.

Step 4: Conclusion
The increase is 2 times the original energy. Final Answer: (B)