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Is Matter Around Us Pure

Question
CBSEENSC9005970

A rifle of mass 3 kg fires a bullet of mass 0.03 kg. The bullet leaves the barrel of the rifle at a velocity of 100 m/s. If the bullet takes 0.003 s to move through its barrel, calculate the force experienced by the rifle due to its recoil.

Solution
bold For bold space bold bullet bold comma bold space

Mass comma straight m subscript 1 space equals space 0.03 space kg

Initial space velocity comma space straight u subscript 1 space equals space 0 space straight m divided by straight s

Final space velocity comma space straight v subscript 1 space equals space 100 space straight m divided by straight s

bold For bold space bold rifle bold comma bold space

Mass comma space straight m subscript 2 space equals space 3 space kg space

Initial space velocity comma space straight u subscript 2 space equals space 0 space straight m divided by straight s

Final space velocity comma space straight v subscript 2 space equals space ? space

Now comma space according space to space law space of space conservation space of space mometum comma space

space space space space space space space space straight m subscript 1 straight u subscript 1 space plus space straight m subscript 2 straight u subscript 2 space equals space straight m subscript 1 straight v subscript 1 space plus space straight m subscript 2 straight v subscript 2

rightwards double arrow space space space space space space 0 space plus space 0 space equals space 0.03 space cross times 100 plus 3 cross times straight v subscript 2

rightwards double arrow space space space space space space space space straight v subscript 2 space equals space minus fraction numerator 0.03 cross times 100 over denominator 3 end fraction space equals space minus 1 space straight m divided by straight s space

Negative space sign space indicates space that space the space rifle space moves space in space straight a space direction space
opposite space to space that space of space bullet. space

Force space exerted space on space the space rifle space is comma space

straight F space equals space straight m subscript 2 open parentheses fraction numerator straight v subscript 2 space minus space straight u subscript 2 over denominator straight t end fraction close parentheses

space space space space equals space 3 space open parentheses fraction numerator negative 1 minus 0 over denominator 0.003 end fraction close parentheses space

space space space space equals space minus space 1000 space straight N

Negative space sign space again space indicates space taht space the space force space of
space recoil space left parenthesis backward space kick right parenthesis space on space the space gun. space