In a simple pendulum of length l the bob is pulled aside

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In a simple pendulum of length l the bob is pulled aside from its equilibrium position through an angle θ and then released. The bob passes through the equilibrium position with speed

1. √2gl( 1 + cos θ )
2. √2gl sin θ
3. √2gl
4. √2gl( 1 - cos θ )

Correct Option: D

If l is length of pendulum and θ be angular amplitude then height

h = AB - AC = l – l cos θ = l(1 – cos θ)
At extreme position, potential energy is maximum and kinetic energy is zero; At mean (equilibrium) position potential energy is zero and kinetic energy is maximum, so from principle of conservation of energy.
(KE + PE) at P = (KE + PE) at B

0 + mgh =	1	mv² + 0
	2

⇒ v = √2gh = √2gl(1 – cos θ)