Question

if A bullet of mass 0.01 kg is fired from a gun of mass 5kg and speed of bullet is 250ms. Find recoil of gun​

Answer 1

$\huge\mathfrak\purple{Answer ;}$

So,

Mass of Bullet × velo. of Bullet = Mass of gun × velo. of Gun

0.01 × 250 = 5 × v

2.5/5 = v

0.5 = v.

Hence, Recoil Velocity will be 0.5 ms-1

Answer 2

$\bigstar\bf\blue{ANSWER}\bigstar$

$\bigstar\: \: \bf\red{GIVEN}\bigstar$

$\bigstar\rm\red{BEFORE\:FIRING}$

• $\rm\blue{Mass\:of\:Bullet(m_1)=0.01kg}$

• $\rm\blue{Mass\:of\:gun(m_2)=5kg}$

• $\rm\blue{initial\:velocity\:of\:the\:bullet(u_1)=0}$

• $\rm\blue{initial\:velocity\:of\:the\:gun(u_2)=0}$

Now,

$\bigstar\rm\red{AFTER\:FIRING}$

• $\rm\blue{Mass\:of\:Bullet(m_1)=0.01kg}$

• $\rm\blue{Mass\:of\:gun(m_2)=5kg}$

• $\rm\blue{Final\:velocity\:of\:the\:bullet(v_1)=250m/s^{-1}}$

• $\rm\blue{Final\:velocity\:of\:the\:gun(v_2)=?}$

Now, According to the law of conservation of momentum,Momentum of the system is Conserved.

$\textbf{Total Momentum before firing=Total Momentum after firing}$

$\implies\bf\red{m_1u_1+m_2u_2=m_1v_1+m_2v_2}$

$\implies\bf\red{(0.01)×(0)+(5)(0)=(0.01)×(250)+(5)×v_2}$

$\implies\bf\red{0=2.5+5v_2}$

$\implies\bf\red{-2.5=5v_2}$

$\implies\bf\red{v_2=\dfrac{\cancel{-2.5}}{\cancel{5}}}$

$\implies\bf\red{v_2=0.5m/s^{-1}}$

Thus,The recoil Velocity of the gun will be 0.5m/s^-1