(C) Since the initial momentum of the system is zero,the final momentum must also be zero according to the law of conservation of linear momentum.Let

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(C) Since the initial momentum of the system is zero,the final momentum must also be zero according to the law of conservation of linear momentum.Let the velocity of the mass $2M$ be $\vec{v} = u_x \hat{i} + u_y \hat{j}$.The momentum along the $X$-axis is: $M(4) + M(0) + 2M(u_x) = 0 \Rightarrow 2M u_x = -4M \Rightarrow u_x = -2 \ m s^{-1}$.The momentum along the $Y$-axis is: $M(0) + M(6) + 2M(u_y) = 0 \Rightarrow 2M u_y = -6M \Rightarrow u_y = -3 \ m s^{-1}$.The magnitude of the velocity $u$ is given by $u = \sqrt{u_x^2 + u_y^2}$.$u = \sqrt{(-2)^2 + (-3)^2} = \sqrt{4 + 9} = \sqrt{13} \ m s^{-1}$.

Class 11 Physics Newton's Laws of Motion and Friction Conservation of Linear Momentum

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$A$ particle of mass $4 M$ which is initially at rest explodes into three pieces of masses $M, M$ and $2 M$. The equal masses move along $X$ and $Y$-axes with velocities $4 \ m s^{-1}$ and $6 \ m s^{-1}$ respectively. The magnitude of the velocity of the heavier mass is

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A
$\sqrt{17} \ m s^{-1}$
B
$2 \sqrt{13} \ m s^{-1}$
C
$\sqrt{13} \ m s^{-1}$
D
$\frac{\sqrt{13}}{2} \ m s^{-1}$

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Newton's Laws of Motion and Friction

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Conservation of Linear Momentum

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$A$ shell in free space initially at rest explodes into two pieces,$A$ and $B$,which then move in opposite directions. Piece $A$ has less mass than piece $B$. Ignore all external forces. Identify the correct statement.

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Two ice skaters $A$ and $B$ approach each other at right angles. Skater $A$ has a mass $30 \, kg$ and velocity $1 \, m/s$,and skater $B$ has a mass $20 \, kg$ and velocity $2 \, m/s$. They meet and cling together. Their final velocity of the couple is ............. $m/s$.

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$A$ particle of mass $4 M$ which is initially at rest explodes into three pieces of masses $M, M$ and $2 M$. The equal masses move along $X$ and $Y$-axes with velocities $4 \ m s^{-1}$ and $6 \ m s^{-1}$ respectively. The magnitude of the velocity of the heavier mass is

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$A$ bomb is projected upwards. At its topmost point,it explodes into three identical fragments. The first fragment reaches the ground in $10 \ s$,and the other two reach the ground in $20 \ s$ each. Find the maximum height $h$ reached by the original bomb. (in $m$)

$A$ bullet of mass $5 \,g$ is shot from a gun of mass $5 \,kg$. The muzzle velocity of the bullet is $500 \,m/s$. The recoil velocity of the gun is ........... $m/s$.

$A$ shell in free space initially at rest explodes into two pieces,$A$ and $B$,which then move in opposite directions. Piece $A$ has less mass than piece $B$. Ignore all external forces. Identify the correct statement.

Two ice skaters $A$ and $B$ approach each other at right angles. Skater $A$ has a mass $30 \, kg$ and velocity $1 \, m/s$,and skater $B$ has a mass $20 \, kg$ and velocity $2 \, m/s$. They meet and cling together. Their final velocity of the couple is ............. $m/s$.

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