Question

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$\red{\bigstar} \: \: {\large{\pmb{\sf{\underline{Very \: Easy \: Physics \: Question...}}}}}$

A bullet of mass ${\sf{20 \: grams}}$ is horizontally fired with the velocity ${\sf{150 \: ms^{-1}}}$ from a pistol of mass ${\sf{2 \: kg}}$ What is the recoil velocity of the pistol?

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⠀⠀⠀⠀⠀⠀Solution of the question is -1.5 m/s. So kindly answer with explanation. ​

Answer 1

$\large \frak{given}\begin{cases} \sf mass_{(bullet)} = \frak{20 gm} = \frak{ \red{0.02 kg}} \\ \sf initial \: velocity_{(bullet)} = \frak{0 \: ms ^{ - 1} } \\ \sf final \: velocity_{(bullet)} = \frak{150 \: {ms}^{ - 1} } \\ \sf mass_{(gun)} = \frak{2kg} \\ \sf initial \: velocity_{(gun)} = \frak{0 \: {ms}^{ - 1} }\end{cases}$

❍ initial velocities of gun and bullet are 0m/s respectively. This is because they both are kept at rest.

❍ We are asked to find the value of recoil velocity of gun or the final velocity of gun.

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$\bigstar \large \underline{ \rm \pink{{ \sf concept : - }}}$

• In this question we are going to use the concept of law of conservation of momentum. Which states that:-
• For two or more bodies, their total momentum remains constant unless an external force is applied. Therefore, momentum can neither be created nor destroyed.
• This can also be explained by an example of two colliding balls.
• Suppose we have two balls one having a mass of $\sf m_{1}$ whose initial and final velocities are $\sf u_{1}m/s\: and\: v_{1}$ m/s respectively.
• Consider the mass of another ball as $\sf m_{2}$ kg whose initial and final velocities are $\sf u_{2}m/s \:and \:v_{2} m/s$
• Now, Law if conservation of momentum states that, the total momentum of both the balls before collision is equal to the total momentum of the balls after collision.

We know that:-

$\underline{ \boxed{ \pink{{ \frak{momentum( \rho) = mass(m) \times velocity(v)}}}}} \bigstar$

Henceforth, Law of Conservation of momentum can be equated as:-

$\underline{ \boxed{ \pink{ \frak{m_{1}u_1 + m_2u_2 = m_1v_1 + m_2v_2}}}} \bigstar$

• This Question is simply formula bases as we are already provided with all the values and we just have to calculate the recoil velocity of gun.

$\: \: \: \: \: \: \dag \: \underline{ \frak{substituting \: the \: given \: values \: in \: formula : - }}$

$: \implies \sf (0.02)(0) + (2)(0) = (0.02)(150) + (2)(v_2)$

$: \implies \sf 0 = 3 + 2v_2$

$: \implies \sf - 3 = 2v_2$

$: \implies {\boxed{ \pink{{ \frak{v_ 1 = 1.5 {ms}^{ - 1} }}}}} \bigstar$

$\therefore\underline{ \sf the \: required \: answer \: is \: - 1.5 {ms}^{ - 1} }$

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I hope it's beneficial :D

Answer 2

Explanation:

Initial momentum of the system is 0 as it is at rest.

⟹V=1.5m/s

Please refer to the attachment!!

Hope it helps!!

Thank you