A 40 kg mass, hanging at the end of a rope of length l, oscillates in a vertical plane with an angular amplitude `theta_0.` What is the tension in the rope when it makes en angle `theta` with the vertical ? If the breaking strength of the rope is 80 kg, what is the maximum amplitude with which the mass can oscillate without the rope breaking?

Explanation

At position (1),`u=0`
`v^(2)=u^(2)+2gh=0+2gL(cos theta-costheta_(0))`
`T-mg cos theta=(mv^(2))/(L)=(m)/(L)xx2gL(costheta-costheta_(0))`
`T=mg[cos theta+2costheta-2costheta_(0)]`
`=3mg cos theta-2mg cos theta_(0)`
`=120g cos theta-80g cos theta_(0)`
when the mass is at the lowest point, tension in the string is maximum,
`theta=0,T=T_(max)=80g`
`T=120gcostheta-80g costheta_(0)`
`T_(max)=120g cos theta-80g cos theta_(0)`
`80g=120g-80g cos theta_(0)=(1)/(2)impliestheta_(0)=60^(@)`