An explosion breaks a rock into three parts i | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(D) According to the law of conservation of linear momentum,the initial momentum of the rock is zero. Therefore,the vector sum of the momenta of the t

Vedclass · Accepted Answer

$5$

Vedclass · Answer

(D) According to the law of conservation of linear momentum,the initial momentum of the rock is zero. Therefore,the vector sum of the momenta of the three parts must be zero.Let the momenta of the three parts be $\vec{p}_1$,$\vec{p}_2$,and $\vec{p}_3$.$\vec{p}_1 + \vec{p}_2 + \vec{p}_3 = 0 \implies \vec{p}_3 = -(\vec{p}_1 + \vec{p}_2)$.The magnitude of the momentum of the first part is $p_1 = m_1 v_1 = 1 \, kg 	imes 12 \, m s^{-1} = 12 \, kg \, m s^{-1}$.The magnitude of the momentum of the second part is $p_2 = m_2 v_2 = 2 \, kg 	imes 8 \, m s^{-1} = 16 \, kg \, m s^{-1}$.Since the two parts move at right angles to each other,the magnitude of the resultant momentum of these two parts is $p_{12} = \sqrt{p_1^2 + p_2^2} = \sqrt{12^2 + 16^2} = \sqrt{144 + 256} = \sqrt{400} = 20 \, kg \, m s^{-1}$.The third part must have a momentum equal in magnitude and opposite in direction to this resultant momentum to satisfy the conservation law.Thus,$p_3 = p_{12} = 20 \, kg \, m s^{-1}$.Given the speed of the third part $v_3 = 4 \, m s^{-1}$,its mass $m_3$ is:$m_3 = \frac{p_3}{v_3} = \frac{20 \, kg \, m s^{-1}}{4 \, m s^{-1}} = 5 \, kg$.

Similar Questions

$A$ stationary body explodes into two parts of masses $M_1$ and $M_2$. They move in opposite directions with velocities $V_1$ and $V_2$. The ratio of their kinetic energies is

$A$ body of mass $0.25 \, kg$ is projected with a muzzle velocity of $100 \, m/s$ from a tank of mass $100 \, kg$. What is the recoil velocity of the tank in $m/s$?

$A$ bomb of mass $3m \text{ kg}$ explodes into two pieces of mass $m \text{ kg}$ and $2m \text{ kg}$. If the velocity of the $m \text{ kg}$ mass is $16 \text{ m/s}$,the total kinetic energy released in the explosion is ................. $m \text{ J}$.

$A$ system of $N$ particles is free from any external forces. Which of the following is true for the magnitude of the total momentum of the system?

$A$ particle of mass $m$ is moving along the $x$-axis with a speed $v_0$. Suddenly,a part of its mass,$m/3$,breaks off and moves parallel to the $y$-axis with a speed $2v_0$. Find the velocity of the remaining part in terms of unit vectors.

Vedclass Test Series

Exam Paper Generator

Online Exam Module