Astring is stretched between two trees so that it is initially horizontal. when a bird lands in the middle of the string and comes to rest (deflecting the string down a tiny bit in the middle), the tension in the string will:

Explanation:

Lets take weight of the bird = wt

Tension in the string = T

2 T cosθ = wt

As we know that  

If angle θ is so small then we can say that

cosθ = 1

⇒2 T x 1  = wt  

2 T = wt

Therefore the tension in the string will be half of the weight.

T = Mg / (2 CosФ)

Explanation:

Let m be the mas of the bird T be the tension and Ф be the angle between the string and the vertical.

According to the diagram, the components of the tension force

T CosФ + T Cos Ф = Mg

2T CosФ = Mg

T = Mg / (2 CosФ)

because growing process had stoped after 4-5 year