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

Answers (1)

best_answer

By linear momentum conservation

$m_{1}u_{1}+m_{2}u_{2}= m_{1}V_{1}+m_{2}V_{2}\\$

$10\times 10^{-3}\left ( V\right )+1(0)= 10^{-2}\times (-100)+(1)V_{2}\\$

$V_{2}= 1+10^{-2}V$

For the Bob to just complete the vertical circular motion

$V_{2}= \sqrt{5gR}$

here $R= l= 0.5\\$

$1+10^{-2}V= \sqrt{25}\\$

$1+10^{-2}= V5\\$

$\Rightarrow V= 400(m/s)$

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vishal kumar

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