Question

A bullet of mass 50 g is fired with a velocity of 250 ms-1 . If the mass of the rifle is 5 kg, calculate
the recoiling velocity of the rifle

Answer 1

Provided that:

• Mass of bullet = 50 grams
• Velocity of bullet = 250 m/s
• Mass of rifle = 5 kilograms

To calculate:

• The recoil velocity of the rifle

Solution:

• Recoil velocity of the rifle = 2.5 m/s

Using concept:

• Momentum formula

• Law of conservation of momentum

• Formula to convert g into kg

Using formula:

• p = mv
• p of 1st object = p of 2nd object
• 1 g = 1/1000 kg

Where, p denotes momentum, m denotes mass of the object, v denotes velocity.

Here, the 1st object is bullet and the 2nd object is the rifle.

Required solution:

~ Firstly let us convert grams into kilograms!

→ 1 gram = 1/1000 kilograms

→ 50 grams = 50/1000 kilograms

→ 50 grams = 5/100 kilograms

→ 50 grams = 0.05 kilograms

~ Now let us calculate the momentum of the given bullet!

→ Momentum = Mass × Velocity

→ p = mv

→ p = 0.05(250)

→ p = 0.05 × 250

→ p = 12.5 kg m/s

→ Momentum = 12.5 kg m/s

~ Now let us calculate the momentum of given rifle! Let the velocity of rifle is v

→ Momentum = Mass × Velocity

→ p = mv

→ p = 5(v)

→ p = 5 × v

→ p = 5v kg m/s

→ Momentum = 5v kg m/s

~ Now let us find out the recoil velocity of the rifle by using Law of conservation of momentum!

→ p of 1st object = p of 2nd object

→ 12.5 = 5v

→ 12.5/5 = v

→ 2.5 = v

→ v = 2.5 m/s

→ Recoil velocity = 2.5 m/s

Additional information:

★ Momentum - It is that property of a moving body and is defined of mass and velocity of the body. It's a vector quantity. SI unit is kg m/s

$\: \: \: \: \: \: \:{\sf{Momentum = \: Mass \times Velocity}} \: \: \green \star$

Answer 2

Answer:-

• Mass of bullet=50g=0.05kg=m1
• Velocity of bullet=250m/s=u
• Mass of rifle=4kg=m2
• Recoil velocity of rifle=v=?

Now

• Momentum=P

We know

$\boxed{\sf P=MV}$

According to law of conservation of linear momentum,

$\boxed{\sf \triangle P=P}$

$\\ \rm\longmapsto m_1u=m_2v$

$\\ \rm\longmapsto 0.05\times 250=5v$

$\\ \rm\longmapsto v=\dfrac{0.05\times 250}{5}$

$\\ \rm\longmapsto v=0.05\times 50$

$\\ \rm\longmapsto\underline{\boxed{\bf{ v=2.5m/s}}}$

Hence

• Recoil velocity of the rifle is 2.5m/s.