A machine gun is mounted on a $2000 \,kg$ car on a horizontal frictionless surface. At some instant the gun fires bullets of mass $10\, gm$ with a velocity of $500 \,m/sec$ with respect to the car. The number of bullets fired per second is ten, the acceleration of the car will be .....$\,m/{\sec ^2}$
A machine gun is mounted on a $2000 \,kg$ car on a horizontal frictionless surface. At some instant the gun fires bullets of mass $10\, gm$ with a velocity of $500 \,m/sec$ with respect to the car. The number of bullets fired per second is ten, the acceleration of the car will be .....$\,m/{\sec ^2}$
$0.25$
$2.5$
$5.0$
$0.025$
A machine gun is mounted on a $2000 \,kg$ car on a horizontal frictionless surface. At some instant the gun fires bullets of mass $10\, gm$ with a velocity of $500 \,m/sec$ with respect to the car. The number of bullets fired per second is ten, the acceleration of the car will be .....$\,m/{\sec ^2}$
$u $ = velocity of bullet
$\frac{{dm}}{{dt}} = $ Mass thrown per second by the machine gun
$= $Mass of bullet $×$ Number of bullet fired per second
$ = 10\;g \times 10\;bullet/\sec $$ = 100\;g/\sec \; = \;0.1\;kg/\sec $
$\therefore $ Thrust $ = \frac{{udm}}{{dt}} = 500 \times 0.1 = 50\;N$
Acceleration of the car $ = \frac{{{\rm{Thrust \,on \,the \,car}}}}{{{\rm{Mass \,of\, the\, car}}}}$
$ = \frac{{50}}{{2000}} = \frac{1}{{40}} = 0.025\;m/{s^2}$
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