Educational Statistics (Mean, Median, Mode)
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With reference to the motion and mechanics of a simple pendulum, consider the following statements:
- 1. The time period of a simple pendulum does not depend on the mass and size of its bob; rather, it depends only on the effective length of the pendulum and the acceleration due to gravity ($g$) at that place.
- 2. If the effective length of a simple pendulum is increased four times, its time period becomes double, while its frequency remains halved.
- 3. When a simple pendulum moves from its extreme position towards the mean position, its potential energy continuously decreases and kinetic energy increases, keeping the total mechanical energy conserved.
- 4. If a simple pendulum is suspended in a lift that is moving with an upward acceleration, the time period of that pendulum will increase because the value of effective acceleration due to gravity decreases.
Which of the above statement(s) is/are completely true?
✓ Correct! Well done.
✗ Not quite — the correct answer is highlighted above.
Detailed Explanation
According to the analysis of this question, statements 1, 2, and 3 are completely true. According to statement 1, the time period of a simple pendulum is $T = 2\pi\sqrt{L/g}$, which does not depend on the mass of the bob. According to statement 2, increasing the length four times makes the time period $\sqrt{4} = 2$ times. Statement 3 is based on the law of conservation of energy. However, statement 4 is false because when a lift accelerates upwards, the effective acceleration due to gravity becomes $g' = g + a$, which decreases the time period $T$ (rather than increasing it).
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