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The angular amplitude of a simple pendul...

The angular amplitude of a simple pendulum is `theta_(0)`. The maximum tension in its string will be

A

`mg(1-theta_(0))`

B

`mg(1 + theta_(0))`

C

`mg(1- theta_(0)^(2))`

D

`mg(1 + theta_(0)^(2))`

Text Solution

Verified by Experts

The correct Answer is:
D
Maximum tension
`T = (mv_(B)^(2))/r + mg`
Since, `mgh = 1/2 mv_(B)^(2)`
`rArr v_(B)^(2) = 2gh = 2gl(1- cos theta_(0))`
`therefore T = mg + (2mgl)/l (1- cos theta_(0))`
`= mg + 2 mg xx 2 sin^(2) theta_(0)/2`
For small angle `sin theta = theta`
`T = mg + 4mg xx (theta_(0)/2)^(2) = mg (1 + theta_(0)^(2))`
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