The initial tension T₀ of the belt is equal to-

Explanation:

Initial tension (To):

When a belt is first fitted to a pair of pulleys, an initial tension To is given to the belt when the system is stationary. When transmitting power, the tension on the tight side increases to T1 and that on the slack side decreases to T2.

It is assumed that the material of the belt is perfectly elastic, i.e. the strain in the belt is proportional to the stress in it and the total length of the belt remains unchanged. Therefore, the tension on the tight side will increase by the same amount as the tension on the slack side decreases.

Tension on tight side T1 = To + δT

Tension on slack side T2 = To - δT

where To is the initial tension and T1 and T2 is the tension on the tight and slack side respectively.

Mathematically initial tension is

\(T_o= \frac{{T_1 + T_2 }}{2}\)

 Considering centrifugal tension:

\(T_o= \frac{{T_1 + T_2 +2T_c }}{2}\)