Question

Hello guys!!!


The angular amplitude of a simple pendulum is θo. The maximum tension in its string will be
(a) mg(1-θo)
(b) mg(1+θo)
(c) mg(1-θo^2)
(d) mg(1+θo^2)

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Answer 1

Answer: mg(1 + θ²o)

Explanation:

Tmax = mg + mv²/I .....(1)

When bob of pendulum comes from A to B, it covers a vertical distance h.

∴ cosθo = (I - h)/I

⇒ h = I ( I - cos θ ). .....(2)

Also during A to B , potential energy of bob converts into kinetic energy

∴ mgh = ½mv²

∴

$v = \sqrt[]{2gh} \: \: \: \: \: \: \: \: .....(3)$

Thus, using Eqs. (1), (2) and (3) we obtain

Tmax = mg + 2mg/I ( 1- cosθo )

= mg + 2mg [(1 - 1) + θ²o/2]

(By using binomial theorem)

= mg ( 1+ θ²o )