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JEE Main 202429 JanuaryEvening Shift
Exam
JEE Main
Year
2024
Date
29 January
Shift
Evening Shift
Subject
Physics
Chapter
Work, Power and Energy

JEE Main 2024 · 29 January · Evening Shift · Physics · Work, Power and Energy

The bob of a pendulum was released from a horizontal position. The...

The bob of a pendulum was released from a horizontal position. The length of the pendulum is 10m10m. If it dissipates 1010 % of its initial energy against air resistance, the speed with which the bob arrives at the lowest point is: [Use, g=10ms−2g = 10m{s}^{- 2} ]The bob of a pendulum was released from a horizontal position. The length of the pendulum is 10m . If it dissipates 10

Options

  1. A65ms−16\sqrt{5}m{s}^{- 1}
  2. B56ms−15\sqrt{6}m{s}^{- 1}
  3. C55ms−15\sqrt{5}m{s}^{- 1}
  4. D25ms−12\sqrt{5}m{s}^{- 1}

Correct answer

A. 65ms−16\sqrt{5}m{s}^{- 1}

Step-by-step solution

The bob of a pendulum was released from a horizontal position. The length of the pendulum is 10m . If it dissipates 10

Given the length of the pendulum is ℓ=10mℓ = 10m.

The initial potential energy of the pendulum at the horizontal position is given by

U=mgℓ...(1)U = mgℓ . . . \left(1\right)

The final kinetic energy of the pendulum at the lowermost position is given by

K=12mv2...(2)K = \dfrac{1}{2}m{v}^{2} . . . \left(2\right)

So, from equations (1) and (2), it follows that

910mgℓ=12mv2⇒910×10×10=12v2⇒v2=180⇒v=180=65ms−1\dfrac{9}{10}mgℓ = \dfrac{1}{2}m{v}^{2} ⇒ \dfrac{9}{10} \times 10 \times 10 = \dfrac{1}{2}{v}^{2} ⇒ {v}^{2} = 180 ⇒ v = \sqrt{180} = 6\sqrt{5}m{s}^{- 1}

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