Question

At a place, the length of the oscillating simple pendulum is made $1/4$ times keeping amplitude same then the total energy will be ______.

• A. 2 times
• B. 4 times
• C. 8 times
• D. 16 times

Hint:

Shorter pendulums swing much faster (higher $\omega$). Since Energy scales with the SQUARE of frequency ($E \propto \omega^2$), a pendulum that is 4 times shorter oscillates twice as fast, resulting in 4 times the energy!

Answer 1

The Correct Option is B

Step 1: Understanding the Concept:
The total energy $E$ of a simple pendulum is $E = \frac{1}{2}m\omega^2 A^2$. For a pendulum, $\omega^2 = \frac{g}{L}$.

Step 2: Formula Application:
$E = \frac{1}{2}m(\frac{g}{L})A^2 \implies E \propto \frac{1}{L}$ (when amplitude $A$ and mass $m$ are constant).

Step 3: Explanation:
If the new length $L' = L/4$, then the new energy $E'$ is: $E' \propto \frac{1}{L/4} = 4 \times \frac{1}{L}$. So, $E' = 4E$.

Step 4: Final Answer:
The total energy will become 4 times the original energy.