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 arrives at the lowest point is ______.

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Solution

Q.
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 arrives at the lowest point is ______.

[Use, g = 10 ${ms}^{- 2}$ ] [2024]

1 $6 \sqrt{5} {ms}^{- 1}$

2 $5 \sqrt{5} {ms}^{- 1}$

3 $2 \sqrt{5} {ms}^{- 1}$

4 $5 \sqrt{6} {ms}^{- 1}$

Ans.
(1)

$ℓ = 10 m,$

Initial energy $= m g ℓ$

So, $\frac{9}{10} m g ℓ = \frac{1}{2} m v^{2}$

$\Rightarrow \frac{9}{10} \times 10 \times 10 = \frac{1}{2} v^{2}$

$v^{2} = 180$

$v = \sqrt{180} = 6 \sqrt{5} m/s$

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