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(D) Let $u$ be the velocity of the bullet with respect to the car.The rate of mass ejection $\frac{dm}{dt}$ is the mass thrown per second by the machi

Vedclass · Accepted Answer

$0.025$

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(D) Let $u$ be the velocity of the bullet with respect to the car.The rate of mass ejection $\frac{dm}{dt}$ is the mass thrown per second by the machine gun.$\frac{dm}{dt} = 	ext{Mass of one bullet} 	imes 	ext{Number of bullets fired per second}$$\frac{dm}{dt} = 10 \,g 	imes 10 \,bullets/s = 100 \,g/s = 0.1 \,kg/s$.The thrust force $F$ exerted on the car is given by $F = u \frac{dm}{dt}$.$F = 500 \,m/s 	imes 0.1 \,kg/s = 50 \,N$.The acceleration $a$ of the car is given by $a = \frac{F}{M}$,where $M$ is the mass of the car.$a = \frac{50 \,N}{2000 \,kg} = \frac{1}{40} \,m/s^2 = 0.025 \,m/s^2$.

$A$ machine gun is mounted on a $2000 \,kg$ car on a horizontal frictionless surface. At some instant,the gun fires bullets of mass $10 \,g$ with a velocity of $500 \,m/s$ with respect to the car. If the number of bullets fired per second is $10$,the acceleration of the car will be ..... $m/s^2$.

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