Question

From a rifle of mass 4 kg, a bullet of mass 50 g is fired with an initial velocity of 35 m s–1. Calculate the initial recoil velocity of the rifle.

Answer 1

Step-by-step explanation:

The rifle and the bullet make a system. Since, there is no external force acting on it the momentum of the system should be conserved.

∴m

1

u

1

+m

2

u

2

=m

1

v

1

+m

2

v

2

⇒4×0+(

100

50

)×0=4v+

1000

50

×35

⇒4v=−

20

35

⇒v=−

80

35

m/s

Answer 2

$\large{\underline{\underline{\mathrm \orange{❖\:Given:-}}}}$

　　

• Mass of the rifle = 4 kg

　　

• Mass of the bullet = 0.05 kg

　　

• Velocity of bullet = 35 m/s

　　

$\large{\underline{\underline{\mathrm \green{❖\:To\:Find:-}}}}$

　　

• Recoil Velocity of the rifle

　　

$\large{\underline{\underline{\mathrm \pink{❖\:Solution:-}}}}$

　　

Since, the rifle was initially at the rest so initial momentom of rifle is = 0

　

According to the law of conservation of the momentom,

　

Therefore,

　

　　$\tt:\implies{}$$\sf m1v1 = m2v2$

　　

　　$\tt:\implies{}$$\sf 4 \: kg \times v1 = 0.05 \times 35 \: ms$

　　

　　$\tt:\implies{}$$\sf v1 = 0.005 \times \frac{35}{4} = \frac{1.75}{4}$

　　

　　$\tt:\implies{}$$\sf \boxed {v1 = 0.4375 \: m/s}$

　　

$\star\rm\underline\blue{\:Hence,\:Recoil\:velocity\:of\:rifle\:is\:0.4375\:m/s.}$