Question

A ball of mass `m` is attached to a fixed point by a light inextensible string describe a circle in a verticle plane. The tension in the string has the values `alpha mg` and `beta mg`, respectively, when the particle is at the highest and the lowest point in the path. find the relation between `alpha` and `beta`.

Answer 1

`v^(2)=u^(2)-2gxx2L=u^(2)-4gL`
At the lowest point:
`T_(1)-mg=(mu^(2))/(L)`
`T_(1)-mg=(mu^(2))/(L)`
`betamg=mg+(mu^(2))/(L)implies(mu^(2))/(L)=(beta-1)mg`
`T_(2)+mg=(mv^(2))/(L)`
`alphamg+mg=(m)/(L)(u^(2)-4gL)`
`(alpha+1)mg=(mu^(2))/(L)-4mg`
`(alpha+1)mg=(m u^(2))/(L)-4mg`
`=(beta-1)mg-4mg`
`alpha+1=beta-1-4`
`alpha+1=beta-5impliesbeta=alpha+6`