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?

Options

A. `T_("max")=mg[1+((A)/(l))^(2)]`
B. `T_("max")=mg[1-((A)/(l))^(2)]`
C. `T_("max")=mg[1-((l)/(A))^(2)]`
D. `T_("max")=mg[1+((l)/(A))^(2)]`

Answer

A

Explanation

`T=mgcostheta+(mv^(2))/(r)`
`v_(max)=Aomegaandcos=1`
`therefore T_(max)=mg+(mv_(max)^(2))/(r)`
`theta=(x)/(l)andr=l`
`T_(max)=mg+(mA^(2)omega^(2))/(l)=mg+(mA^(2)g)/(l^(2))`
`=mg[1+(A^(2))/(l^(2))]=mg[1+((A)/(l))^(2)]`