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एक $50\, g$ द्रव्यमान की गोली $4\, kg$ द्रव्यमान की रायफ़ल से $35\, m s ^{-1}$ के प्रारंभिक वेग से छोडी जाती है। रायफ़ल के प्रारंभिक प्रतिक्षेपित वेग की गणना कीजिए।
$0.8375$
$0.1023$
$0.4375$
$0.6523$
Solution
Mass of the rifle, $m_1 = 4\,kg$
Mass of the bullet, $m_2 = 50\,g = 0.05\, kg$
Recoil velocity of the rifle $= v_1$
Bullet is fired with an initial velocity, $v_2 = 35\, m/s$
Initially, the rifle is at rest.
Thus, its initial velocity, $v = 0$
Total initial momentum of the rifle and bullet system $= (m_1 + m_2)v = 0$
Total momentum of the rifle and bullet system after firing:
$=m_{1} v_{1}+m_{2} v_{2}=4\left(v_{1}\right)+0.05 \times 35=4 v_{1}+1.75$
According to the law of conservation of momentum:
Total momentum after the firing = Total momentum before the firing $4v_1 + 1.75 = 0$
$ v_1 = -1.75/4 = -0.4375\, m/s$
The negative sign indicates that the rifle recoils backwards with a velocity of $0.4375 \,m/s$.
