Question

A gun of mass M fires a bullet of mass m with a velocity v relative to the gun. The average force required to bring the gun to rest in 0.5 sec. is

Moderate

Solution

Absolute velocity of the bullet , $V_{b} = V - V_{g}$ ……….. $(1)$

$M{V_g} = m{V_b}.............(2)$

From equations $(1) a n d (2)$
$V = \left( {\frac{M}{m}{V_g} + {V_g}} \right)$

${V_g} = \frac{{Vm}}{{M + m}};\;F = \frac{{M{V_g}}}{t}$

$F = \frac{M}{{{\raise0.5ex\hbox{$\scriptstyle 1$} \kern-0.1em/\kern-0.15em \lower0.25ex\hbox{$\scriptstyle 2$}}}} \times \frac{{mV}}{{m + M}} = \frac{{2MmV}}{{M + m}}$

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