Consider the tension in each string is T.
When you draw the free body diagram of the sphere, the weight of sphere mg acts downwards and T acts along each string
The net acceleration of the sphere is towards the center (centripetal acceleration).
So
there is no vertical acceleration.
Thus
mg = Tcos60 + Tsin60
T = mg/(cos60 + sin60)
= 3.7*9.81/(cos60 + sin60)
T = 26.57 N
Therefore, the closest option is fourth option is correct.
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