Question

A bullet of \(10~g\), moving with velocity \(\upsilon ,\) collides head-on with the stationary bob of a pendulum and recoils with velocity \(100~\text{m/s}.\) The length of the pendulum is \(0.5~\text m\) and mass of the bob is \(1~\text{kg}\). The minimum value of \(\upsilon \) = __________ \(\text{m/s}\) so that the pendulum describes a circle.
(Assume the string to be inextensible and \(g=10\text{ m/s}^{2}\))

• A. 400.0
• B. 400.00
• C. 400

Answer 1

Answer: (A), (B), (C)

Minimum value of velocity of the bob so that it describes a complete circle is $v=\sqrt{5gl}$
Here length of pendulum is $l=0.5\text{m}$
Hence, $v=\sqrt{5g\left(0.5\right)}=5\text{m/s}$
Final momentum of bob after collision should be $5\text{kg m/s}$
initial momentum of bullet before collision is $m_b\upsilon ={10}^{-2}\upsilon \text{kg m/s}$
Final momentum of bullet after collision is $m_b(-100)=-1\text{kg m/s}$

Applying conservation of momentum,

Initial momentum= Final momentum

${10}^{-2}\upsilon =5-1=4$
$\upsilon =400\text{m/s}$