Question

A bullet of mass 30 gis fired from a gun with a velocity of 160 ms. If the recoil velocity of the gun is 2 ms
then what is the mass of the gun​

Answer 1

Given :

▪ Mass of bullet = 30g

▪ Velocity of bullet = 160m/s

▪ Recoil velocity of gun = 2m/s

To Find :

▪ Mass of the gun.

Concept :

☞ Since, no net force acts on the system, we can easily apply concept of momentum conservation to solve this question.

$\implies\sf\:(P_i)_b+(P_i)_g=(P_f)_b+(P_f)_g\\ \\ \implies\sf\:0 + 0=(P_f)_b+(P_f)_g\\ \\ \implies\bf\:(P_f)_b+(P_f)_g=0$

• $\sf{(P_i)_b}$ denotes Initial momentum of bullet
• $\sf{(P_i)_g}$ denotes initial momentum of gun
• $\sf{(P_f)_b}$ denotes final momentum of bullet
• $\sf{(P_f)_g}$ denotes final momentum of gun

Conversion :

▪ 1000g = 1kg

▪ 30g = 30/1000 = 0.03kg

Calculation :

$\dashrightarrow\sf\:(P_f)_b+(P_f)_g=0\\ \\ \dashrightarrow\sf\:mv+MV=0\\ \\ \dashrightarrow\sf\:[0.03\times 160] + [M\times (-2)]=0\\ \\ \dag\sf\:\blue{-ve\:sign\:shows\:opposite\:direction}\\ \\ \dashrightarrow\sf\:M=\dfrac{0.03\times 160}{2}\\ \\ \dashrightarrow\underline{\boxed{\bf{\green{M=2.4\:kg}}}}\:\orange{\bigstar}$

Answer 2

Given:-

Mass of the bullet = 30 g

Velocity of the bullet = 160 m/s

recoil velocity of the gun = 2m/s

Find out:-

Mass of the gun =?

Conversion :-

1000g = 1kg

${\tt{ 30 g = \frac{30}{1000} = 0.03kg}}$

Calculation:-

${\implies{\tt{ (p_f)_b + (p_f)_g = 0 }}}$

${\implies{\tt{ mv + MV = 0}}}$

${\implies{\tt{[0.03 ×160] + [M × (-2)] = 0}}}$

${\implies{\tt{ M = \frac{0.03×160}{2}}}}$

$\large\longrightarrow{\underline{\boxed{\mathtt{\color{crimson}{ M = 2.4kg}}}}}{\color{orange}{\bigstar}}$