A simple pendulum of length ‘l’ carries a bob of mass ‘m’. If the breaking strength of the string is 2 mg…

Q: A simple pendulum of length ‘l’ carries a bob of mass ‘m’. If the breaking strength of the string is 2 mg, the maximum angular amplitude from the vertical can be

(a) 0°

(b) 30°

(c) 60°

(d) 90°

Ans: (c)

Sol: As we know , the maximum tension is at the lowest point.

Tmax = 2 m g

T- mg = mv2/l

2mg – mg = mv2/l

v = √(gl)

Applying energy conservation

$ \displaystyle mgl(1-cos\theta) = \frac{1}{2}m(\sqrt{gl})^2$

Cosθ = 1/2

θ= 60°