A simple pendulum of length \(\frac{10}{3}\) meter with a bob of mass \(3 \mathrm{~m}\) is hanging freely from a rigid support. A bullet of mass ' \(\mathrm{m}\) ' is fired with a velocity \(50 \mathrm{~ms}^{-1}\) from the ground at an angle ' \(\theta\) ' with the horizontal. When the bullet is at its highest point of its trajectory, it collides head on with the bob of the pendulum and gets embedded in the bob. After collision, if the pendulum moves through a maximum angle of \(120^{\circ}\), then the value of ' \(\theta\) ' is \(\left(\mathrm{g}=10 \mathrm{~ms}^{-2}\right)\)

1. A \(\cos ^{-1}(0.8)\)
2. B \(\cos ^{-1}(0.6)\)
3. C \(\cos ^{-1}(0.4)\)
4. D \(\cos ^{-1}(0.3)\)