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JEE Main 2024 (29 Jan, Shift 2) · Simple Pendulum

Simple Pendulum question from JEE Main 2024 (29 Jan, Shift 2)

Q39JEE Main 2024 · 29 JAN · SHIFT 2Medium

Simple Pendulum

The bob of a pendulum was released from a horizontal position. The length of the pendulum is 10 m10\text{ m}. If it dissipates 10%10\% of its initial energy against air resistance, the speed with which the bob arrives at the lowest point is:

[Use, g:10 m s−2g : 10\text{ m s}^{-2}]

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Answer: (d)

  1. Released from horizontal, so the drop to the lowest point is L=10 mL = 10\text{ m}.
  2. Only 90%90\% of mgLmgL becomes KE: 12mv2=0.9 mgL\frac{1}{2}mv^2 = 0.9\,mgL.
  3. v2=2×0.9×10×10=180⇒v=180v^2 = 2 \times 0.9 \times 10 \times 10 = 180 \Rightarrow v = \sqrt{180}.
  4. So the answer is (d) 65 m s−16\sqrt{5}\text{ m s}^{-1}.
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