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A simple pendulm has a length L and a bo...

A simple pendulm has a length L and a bob of mass M. The bob is vibrating with amplitude a .What is the maximum tension in the string?

A

`(mg)/(2)`

B

`(mg)/(2) [1+ 2 ((A)/(L))^(2)]`

C

`mg [1+ ((A)/(L))^(2)]`

D

`(mg)/(2) [1 + ((A)/(L))^(2)]`

Text Solution

Verified by Experts

The correct Answer is:
C
`V_("max") = A omega`
`omega = (2pi)/(T) = sqrt((g)/(L))`
`V_("max") = A sqrt((g)/(L))`
`T_("max") - mg = (m(V_("max"))^(2))/(L)` ….(2)

By (1) and (2), `T_("max") = mg + mg(A^(2))/(L^(2)) therefore T_("max") = mg (1 + (A^(2))/(L^(2)))`
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