A pendulum of length 2m consists of a wooden bob of mass 50g . A...

For the bob to completer the vertical circle, ${v}_{b} = \sqrt{5gl}$.

From the conservation of momentum,

${m}_{1}v = {m}_{2}{v}_{b} + {m}_{1}\dfrac{v}{3} ⇒ 75v = 50\sqrt{5gl} + 75\left(\dfrac{v}{3}\right)$

$⇒ 75\left(\dfrac{2v}{3}\right) = 50\sqrt{5 \times 10 \times 2}$

$⇒ 75\left(\dfrac{2v}{3}\right) = 50 \times 10$

$⇒ v = \dfrac{500 \times 3}{150} = \dfrac{500}{50} = 10m{s}^{- 1}$