Question

A 100grams bullet is fired from a 10kg gun with a speed of 1000m/s .what is the speed of recoil of the gun.

Answer 1

Answer:

recoil of gun is -10 m/s

Answer 2

Given :

• Mass of the bullet = 100 g = 0.1 kg
• Mass of the gun = 10 kg
• Speed of the bullet = 1000 m/s

To find :

• Recoil speed of the gun

Solution :

As no external force is acting on the system ( bullet + gun )the momentum of the system remains conserved .

As per law of conservation of momentum ,

Initial momentum of the system = Final momentum of the system

As , initially the system ( bullet + gun) was at rest . As a result , the initial momentum of the system will be zero .

Hence ,

Final momentum of the system = 0

$:\implies P_g + P_b = 0$

$:\implies m_g v_g+ m_b v_b= 0$

here ,

• mg = mass of the gun
• vg = recoil speed of the gun
• mb = mass of the bullet
• vb = speed of the bullet

$:\implies v_g= - \dfrac{ m_b v_b}{ m_g }$

Now let's substitute the given values in the above equation ,

$:\implies v_g= - \dfrac{ 0.1 \times 1000 }{ 10 }$

$:\implies v_g= - \dfrac{ 1000 }{ 100 }$

$:\implies \underline{ \boxed{\red{v_g= - 10 \dfrac{m}{s}} }}$

The recoil speed of the gun is - 10 m/s.