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A pendulum of length 1 m and having a bob of mass 1 g is pulled aside through an angle 60⁰ with the vertical and then released. The power delivered by all the forces acting on the bob when the pendulum makes 30⁰ with the vertical is _____ (g = 10ms^{- 2})

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7.5 mW

24.5 mW

13.5 mW

17.32 mW

answer is A.

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Detailed Solution

Power due to tension is zero.

Power due to mg = $mg \times vcos 60^{o}$

Here,

$v = \sqrt{2 g ∆ h}$

$∆ h = l (\cos 30^{°} - \cos 60^{°}) = 1 (\frac{\sqrt{3}}{2} - \frac{1}{2})$

$∴ v = \sqrt{2 \times 10 \times (\frac{\sqrt{3} - 1}{2})} = \sqrt{10 (\sqrt{3} - 1)} = 2.7 m / s$

We know that power,

$P = \frac{mgv}{2} = \frac{1 \times 10}{2} \times 27 = 13.5 mW$

Hence the correct answer is 13.5mW.

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