Very strange ballistic pendulum problem?

The tension in the wire is determined by using the expression,

T-mg=(mv2f^2)/R

But the final speed after collision is unknown. To determined the final speed we use the law of conservation of energy as follows

Pi=Pf

m1 v1i = m2/m1 v2f -m1f

v1f = (m2/m1)*v2f - v1i

Ki = Kf

1/2 m1v1i^2 = 1/2m1v1f^2 + 1/2 (m2/m1) v2f^2

v1i^2 = (m2/m1)v2f^2 - 2(m2/m1) v2f v1i + v1i^2 + (m2/m1) v2f^2

v2f = 0 (no collision)

(1+m2/m1 ) v2f = 2v1i

v2f = (2v1i)/(1+(m2/m1))

v2f=(14 m/s)/(1+ (5.50kg/2kg))

v2f=3.733 m/s

Now the tension in the wire is determined by,

T - mg = (mv2f^2)/R

T = (mv2f^2)/R+mg = m((v2f^2)/R+g)

T = 5.50kg ((3.733 m/s)^2/1.10m + 9.8 m/s^2 )

T=123.58N

Find initial V of the ornament (pendulum). I'll assume the missile is 2kg. as you have indicated.

(2kg x 14)/(2kg + 5.5kg) = initial V of 3.73m/sec.

The bob mass is now 7.5kg.

Force = mv^2/r, = 7.5 x (3.73^2)/1.1m., = 94.860682N.

Now this is the centripetal force, and the bob is at the bottom of its movement. So add to this force (mg) = 7.5 x 9.8 = 73.5N., and total tension = 168.36N.