well its a good question with simple logic .
condition 1: if there is friction between the rim and the string ---
T1=t2e^u(pi).
u=coeff. of friction.
^ :represents to power.
now,
resultant force of t1 and t2 acts on the rim; T=( t2^2+t1^2+2t1t2 )^1/2=t2(1+e^u(pi)).
condition 2: no friction :
T=t2+t1.
IIT IS NOT A DREAM ,I, CHERISH ABOUT,BUT MY LIFE.........