A particle of mass `1 kg` is attached to a string of length `5 m`. The string is attached to a fixed point `O`. It is released from the position as shown in Fig. Calculate

a. the impulse developed in the string when it becomes taut,
b. the velocity of the particle just after the string becomes taut,
c. the impulse developed in this string `PQ` at this instant.

Explanation

From `M` to `N` the ball will fall a distance o `4m`, then impulse will be developed in the string ON.

velocity of the ball just before the string becomes tight
` u_(0)=sqrt(2xx10xx4)=sqrt(80)m//s`
velocity of the ball in the direction perpendicular to the impulse will remain same (just after and just before the impulse developed.)
`v=u_(0)sintheta=sqrt(80)xx3/5=15/(sqrt(5))m//s`
`J=mu_0costheta=1sqrt(80)xx4/5=16/(sqrt(5)) kgm//s`
`J'=Jsintheta=4/(5sqrt(5))kgm//s`
and impulse given by earth
`J''=Jcostheta=64/(5sqrt(5))kgm//s`