A bullet of mass `m` strikes a pendulum bob of mass `2m` with velocity u es shown in figure. If passes through and emerges but with a velocity `u//2` from bob. The length of the pendulum bob is `l = 2m`. If the minimum value of `u` for which the pendulum bob completes full circle is `10X m//s`, then find `X`.
(Take `g = 10 m//s^(2)`)

Answer

4

Explanation

Let `V` be velocity of mass `2m` just after bullet passes through it. From momentum conservation
`m u + 0 = m((u)/(2)) + 2mV`
`V = (u)/(4)`
For completing circle
`V ge sqrt(5gl) , (u)/(4) ge sqrt(5gl) , u ge 4sqrt(5gl) ge 40 m//s`