A gun fires a small bullet with kinetic energ | vedclass

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Question

(C) According to the law of conservation of linear momentum,the magnitude of momentum of the gun $(p_g)$ and the bullet $(p_b)$ must be equal after fi

Vedclass · Accepted Answer

less than $K$

Vedclass · Answer

(C) According to the law of conservation of linear momentum,the magnitude of momentum of the gun $(p_g)$ and the bullet $(p_b)$ must be equal after firing,i.e.,$p_g = p_b = p$.The kinetic energy $K$ of an object of mass $m$ with momentum $p$ is given by the relation $K = \frac{p^2}{2m}$.Since the momentum $p$ is the same for both the gun and the bullet,we have $K \propto \frac{1}{m}$.Because the mass of the gun $(M)$ is much greater than the mass of the bullet $(m)$,the kinetic energy of the gun $(K_g = \frac{p^2}{2M})$ will be significantly less than the kinetic energy of the bullet $(K_b = \frac{p^2}{2m})$.Therefore,the kinetic energy of the gun is less than $K$.

$A$ gun fires a small bullet with kinetic energy $K$. Then the kinetic energy of the gun while recoiling is

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