A pendulum of length 2 m consists of a wooden bob of mass 50 g . A bullet of mass 75 g is fired towards the stationary bob with a speed v . The bullet emerges out of the bob with a speed v 3 and the b

Question

A pendulum of length 2 m consists of a wooden bob of mass 50 g . A bullet of mass 75 g is fired towards the stationary bob with a speed v . The bullet emerges out of the bob with a speed v 3 and the bob just completes the vertical circle. The value of v is _____ m s - 1 (if g = 10 m s - 2 ).

TestHub · Accepted Answer

For the bob to completer the vertical circle, $v_{b} = \sqrt{5 g l}$ .

From the conservation of momentum,

$m_{1} v = m_{2} v_{b} + m_{1} \frac{v}{3} \Rightarrow 75 v = 50 \sqrt{5 g l} + 75 (\frac{v}{3})$

$\Rightarrow 75 (\frac{2 v}{3}) = 50 \sqrt{5 \times 10 \times 2}$

$\Rightarrow 75 (\frac{2 v}{3}) = 50 \times 10$

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

Physics - Center of Mass Question with Solution | TestHub

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