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The ballistic pendulum is an apparatus u...

The ballistic pendulum is an apparatus used to measure the speed of a fast moving projectile, such as bullet. `A` bullet of mass `m_(1)` is fired into a large block of wood of mass `m_(2)` suspended from light wires. The bullet embeds in the block and the entire system swings through a height `h`. Determine the initial speed of the bullet in terms of `h`?
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Text Solution

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As there is no external force in x-direction, applying conservation of momentum during collision
`m_(1)v_(1)=(m_(1)+m_(2))V_(B)`
`therefore" "V_(B)=(m_(1)v_(1))/(m_(1)+m_(2))`…..(i)
Applying conservation of mechanical energy after collision
`(1)/(2)(m_(1)+m_(2))V_(B)^(2)=(m_(1)+m_(2))=gh`
here `h` is the displacement of center of mass:
`V_(B)=sqrt(2gh)`....(ii)
Form (i) & (ii)
`therefore" "V_(1)=(1+(m_(2))/(m_(1)))sqrt(2gh)`
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