As shown in Fig. 7.67, for vertical equilibrium of mass m
`T "cos" theta = "mg" …… (i) `
While for circular motion
`T "sin" theta = (mv^(2)//r) = mr omega^(2) " " …….. (ii) `
(a) So , from Eqn . (ii) , `T = [ mr omega^(2)//"sin" theta ] = m L omega^(2)`
[as r = L sin `theta`]
`therefore " " T = 10^(-1) xx 1 xx 4^(2) = 1.6 N` [ as `omega = 2 pi f = 2 pi xx ( 2//pi) = 4]`
(b) From Eqn. (i) , cos `theta = ("mg")/(T) = ( 10^(-1) xx 10)/(1.6) = (5)/(8)`,
i.e., `" " theta = cos^(-1) (5 //8)`
(c) `" " v = r omega = L "sin" theta xx omega ` [ as r = L sin `theta`]
or `v = 1 xx 0.78 xx 4 = 3.12` m/s [ as sin `theta = 0.78`]