Let θ be the maximum angular deflection them
1/2mv2 = mg (l - lcosθ)
and T - mg = mv2/l
T = mg + mv2/l
T/πr2 = mg + 2 mg (l - lcosθ)
= 3mg - 2mg cosθ
For maximum value of θ, stress (=T/πr2) must be equal to breaking stress,
i.e., T/πr2 = 7.85 x 108
or, (3mg - 2mg cosθ)/(π x (10-3)2) = 7.85 x 108
or, cosθ = 0.2436 = cos 75.9°
or, θ = 75.9°