A bullet of $25 g$ acquires the velocity of $500 {m s}^{- 1}$ after firing from the gun. Find the recoil velocity of a gun having a mass equal to $5 kg$ .

25 {m s}^{- 1}

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2.5 {m s}^{- 1}

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10 {m s}^{- 1}

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5 {m s}^{- 1}

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Solution

The correct option is B $2.5 {m s}^{- 1}$
Given:
Mass of bullet, $(m_{1}) = 25 g = 0.025 kg$

Velocity of bullet before firing, $(u_{1}) = 0$

Velocity of bullet after firing, $(v_{1}) = 500 {m s}^{- 1}$

Mass of gun, $(m_{1}) = 5 kg$

Velocity of gun before firing, $(u_{2}) = 0$

Velocity of gun after firing = $v_{2}$

We know that, $m_{1} u_{1} + m_{2} u_{2} = m_{1} v_{1} + m_{2} v_{2}$

$0.025 \times 0 + 5 \times 0$ = $0.025 \times 500$ + $5 \times v_{2}$

$0 = 12.5 + 5 \times v_{2}$

$v_{2} = \frac{- 12.5}{5} = - 2.5 {m s}^{- 1}$
Thus, recoil velocity of gun is equal to $2.5 {m s}^{- 1}$ . Here, the negative sign shows that gun moves in the opposite direction of that of the bullet.

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A bullet of 25 g acquires the velocity of 500 m s−1 after firing from the gun. Find the recoil velocity of a gun having a mass equal to 5 kg.

A bullet of $25 g$ acquires the velocity of $500 {m s}^{- 1}$ after firing from the gun. Find the recoil velocity of a gun having a mass equal to $5 kg$ .