Question

From a refill of mass 4kg,a bullet of mass 50g is fired with an interracial velocity of 35 m/s. Calculate the innerracial recole velocity of the refill.

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Answer 1

$\large\underline{\sf{Solution-}}$

Given that,

• From a refill of mass 4kg,a bullet of mass 50g is fired with an initial velocity of 35 m/s.

So,

• Mass of refill, M = 4 km

• Mass of bullet, m = 50 g = 0.05 kg

Since, the refill is at rest. So, initial velocity, u = 0 m/s.

We know,

Momentum = Mass × Velocity.

So, Total initial Momentum of the refill and bullet is given by

$\rm :\longmapsto\:Initial \: Momentum = (m + M) \times 0 = 0$

Let assume that

• Recoil velocity of the refill = V m/s

Given that,

• Velocity of bullet, v = 35 m/s

So,

Total Momentum after bullet is fired is given by

$\rm :\longmapsto\:Total \: Momentum = MV + mv$

$\rm :\longmapsto\:Total \: Momentum = 4 \times V + 0.5 \times 35$

$\rm :\longmapsto\:Total \: Momentum = 4 V + 1.75$

According to Law of Conservation of Momentum,

$\red{\rm :\longmapsto\:(M + m)u = MV + mv}$

On substituting the values, we get

$\red{\rm :\longmapsto\:0 = 4V + 1.75}$

$\red{\rm :\longmapsto\:4V = - 1.75}$

$\red{\rm :\longmapsto\:V = - 0.4375}$

Hence,

• The recoil velocity of the refill is 0.4375 m/s.

Answer 2

Explanation:

Given that,

From a refill of mass 4kg,a bullet of mass 50g is fired with an initial velocity of 35 m/s.

So,

Mass of refill, M = 4 km

Mass of bullet, m = 50 g = 0.05 kg

Since, the refill is at rest. So, initial velocity, u = 0 m/s.

We know,

Momentum = Mass × Velocity.

So, Total initial Momentum of the refill and bullet is given by

\rm :\longmapsto\:Initial \: Momentum = (m + M) \times 0 = 0:⟼InitialMomentum=(m+M)×0=0

Let assume that

Recoil velocity of the refill = V m/s

Given that,

Velocity of bullet, v = 35 m/s

So,

Total Momentum after bullet is fired is given by

\rm :\longmapsto\:Total \: Momentum = MV + mv:⟼TotalMomentum=MV+mv

\rm :\longmapsto\:Total \: Momentum = 4 \times V + 0.5 \times 35:⟼TotalMomentum=4×V+0.5×35

\rm :\longmapsto\:Total \: Momentum = 4 V + 1.75:⟼TotalMomentum=4V+1.75

According to Law of Conservation of Momentum,

\red{\rm :\longmapsto\:(M + m)u = MV + mv}:⟼(M+m)u=MV+mv

On substituting the values, we get

\red{\rm :\longmapsto\:0 = 4V + 1.75}:⟼0=4V+1.75

\red{\rm :\longmapsto\:4V = - 1.75}:⟼4V=−1.75

\red{\rm :\longmapsto\:V = - 0.4375}:⟼V=−0.4375

Hence,

The recoil velocity of the refill is 0.4375 m/s.