Question

# The bob of a simple pendulum is released when its string makes an angle $$\theta$$ with vertical. If the tension in the string is equal to thrice the weight of bob when the bob is at lowest point, the value of $$\theta$$ is:

A
30°
B
45°
C
60°
D
90°

Solution

## The correct option is D $$90°$$Apply WET between A and B,$$mg L( 1 - cos\theta) = \dfrac{1}{2} mv^{2}$$$$v = \sqrt{2gL(1 - cos \theta) }$$At pt. A,$$T - mg = \dfrac{mv^{2}}{L}$$ Also, $$T = 3\ mg$$$$3\ mg - mg = \dfrac{mv^{2}}{L}$$$$\sqrt{2gL} = v = \sqrt{2gL \big(1 - cos \theta\big) }$$$$1 = 1 - cos \theta$$$$cos\theta = 0$$$$\theta = 90^{0}$$Physics

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