The bob of a pendulum was released from a horizontal position. The length of the pendulum is 10 m. If it dissipates 10 of its initial energy against air resistance, the speed with which the bob…

The bob of a pendulum was released from a horizontal position. Th… — Solution | JEE Physics

MCQMediumJEE 2024Kinetic Energy & Work-Energy Theorem

The bob of a pendulum was released from a horizontal position. The length of the pendulum is $10 \, \text{m}$ . If it dissipates $10\%$ of its initial energy against air resistance, the speed with which the bob arrives at the lowest point is:

A
$6\sqrt{5} \, \text{m/s}$
B
$5\sqrt{6} \, \text{m/s}$
C
$5\sqrt{5} \, \text{m/s}$
D
$2\sqrt{5} \, \text{m/s}$

Answer

Correct answer:A

Step-by-step solution

Standard Method

Given: The pendulum length is $\ell = 10 \, \text{m}$ and $10\%$ of the initial energy is dissipated against air resistance.

Find: The speed of the bob at the lowest point.

When the bob is released from the horizontal position, its initial potential energy relative to the lowest point is

E_{\text{initial}} = mg\ell

Using $g = 10 \, \text{m/s}^2$ and $\ell = 10 \, \text{m}$ ,

E_{\text{initial}} = m \cdot 10 \cdot 10 = 100m

Common mistakes

Using height as $2\ell$ instead of $\ell$ is incorrect because the bob is released from the horizontal position, so the vertical drop to the lowest point is exactly $\ell$ . Use $h = \ell$ .
Subtracting $10\%$ from the final speed instead of from the initial energy is wrong because the question states that energy is dissipated. First reduce the energy to $90\%$ of its initial value, then compute the speed from kinetic energy.

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Answer

Step-by-step solution

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