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…

Question

A pendulum of length 2 &#160; m consists of a wooden bob of mass 50 &#160; g . A bullet of mass 75 &#160; 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 &#160; s - 1 (if g = 10 &#160; m &#160; s - 2 ).

Aicharya · Accepted Answer

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

From the conservation of momentum,

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

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

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

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

A pendulum of length 2   m consists of a wooden bob of mass 50   g . A bullet of mass 75   g…

Solution

A pendulum of length 2 &#160; m consists of a wooden bob of mass 50 &#160; g . A bullet of mass 75 &#160; g…

Solution

A pendulum of length 2 m consists of a wooden bob of mass 50 g . A bullet of mass 75 g…