A bullet of $'4\,g'$ mass is fired from a gun of mass $4 \,{kg}$. If the bullet moves with the muzzle speed of $50\, {ms}^{-1}$, the impulse imparted to the gun and velocity of recoil of gun are :

  • [JEE MAIN 2021]
  • A

    $0.4\, {kg} \,{ms}^{-1}, 0.1\, {ms}^{-1}$

  • B

    $0.2 \,{kg} \,{ms}^{-1}, 0.1\, {ms}^{-1}$

  • C

    $0.2 \,{kg} \,{ms}^{-1}, 0.05\, {ms}^{-1}$

  • D

    $0.4 \,{kg}\, {ms}^{-1}, 0.05 \,{ms}^{-1}$

Similar Questions

Two billiard balls of mass $0.05\,kg$ each moving in opposite directions with $10\,ms ^{-1}$ collide and rebound with the same speed. If the time duration of contact is $t=0.005\,s$, then $\dots N$is the force exerted on the ball due to each other.

  • [JEE MAIN 2022]

The balls, having linear momenta $\vec{p}_1=\hat{p} \hat{i}$ and $\vec{p}_2=-p \hat{i}$, undergo a collision in free space. There is no external force acting on the balls. Let $\vec{p}_1^{\prime}$ and $\vec{p}_2^{\prime}$ be their final momenta. The following option$(s)$ is (are) $NOT ALLOWED$ for any non-zero value of $\mathrm{p}, \mathrm{a}_1, \mathrm{a}_2, \mathrm{~b}_1, \mathrm{~b}_2, \mathrm{c}_1$ and $\mathrm{c}_2$.

$(A)$ $ \overrightarrow{\mathrm{p}}_1^{\prime}=\mathrm{a}_1 \hat{\mathrm{i}}+\mathrm{b}_1 \hat{\mathrm{j}}+\mathrm{c}_1 \hat{\mathrm{k}} $

$ \overrightarrow{\mathrm{p}}_2^{\prime}=\mathrm{a}_2 \hat{\mathrm{i}}+\mathrm{b}_2 \hat{\mathrm{j}}$

$(B)$ $ \overrightarrow{\mathrm{p}}_1^{\prime}=\mathrm{c}_1 \hat{\mathrm{k}} $

$ \overrightarrow{\mathrm{p}}_2^{\prime}=\mathrm{c}_2 \hat{\mathrm{k}}$

$(C)$ $ \overrightarrow{\mathrm{p}}_1^{\prime}=\mathrm{a}_1 \hat{\mathrm{i}}+\mathrm{b}_1 \hat{\mathrm{j}}+\mathrm{c}_1 \hat{\mathrm{k}} $

$ \overrightarrow{\mathrm{p}}_2=\mathrm{a}_2 \hat{\mathrm{i}}+\mathrm{b}_2 \hat{\mathrm{j}}-\mathrm{c}_1 \hat{\mathrm{k}}$

$(D)$ $ \vec{p}_1^{\prime}=a_1 \hat{i}+b_1 \hat{j} $

$ \overrightarrow{\mathrm{p}}_2^{\prime}=a_2 \hat{\mathrm{i}}+b_1 \hat{\mathrm{j}}$

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  • [JEE MAIN 2020]

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  • [AIPMT 2013]

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  • [JEE MAIN 2019]