A particle of mass 5m at rest suddenly breaks | vedclass

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

Question

(D) Let the velocity of the third fragment of mass $3m$ be $\vec{v}'$. According to the law of conservation of linear momentum,the initial momentum is

Vedclass · Accepted Answer

$\frac{4}{3} mv^{2}$

Vedclass · Answer

(D) Let the velocity of the third fragment of mass $3m$ be $\vec{v}'$. According to the law of conservation of linear momentum,the initial momentum is zero,so the final momentum must also be zero.$3m \vec{v}' + m v \hat{i} + m v \hat{j} = 0$$3m \vec{v}' = -mv \hat{i} - mv \hat{j}$$\vec{v}' = -\frac{v}{3} \hat{i} - \frac{v}{3} \hat{j}$The magnitude of the velocity of the third fragment is $|\vec{v}'| = \sqrt{(-\frac{v}{3})^2 + (-\frac{v}{3})^2} = \sqrt{\frac{2v^2}{9}} = \frac{\sqrt{2}}{3} v$.The energy released is equal to the total kinetic energy of the fragments:$K = \frac{1}{2} m v^2 + \frac{1}{2} m v^2 + \frac{1}{2} (3m) |\vec{v}'|^2$$K = m v^2 + \frac{3}{2} m (\frac{2v^2}{9}) = m v^2 + \frac{1}{3} m v^2 = \frac{4}{3} m v^2$.

$A$ particle of mass $5m$ at rest suddenly breaks on its own into three fragments. Two fragments of mass $m$ each move along mutually perpendicular directions with speed $v$ each. The energy released during the process is

Similar Questions

State the law of conservation of linear momentum for a system of particles.

$A$ trolley of mass $1000\, kg$ is moving with a velocity of $50\, km/h$. If a mass of $250\, kg$ is added to it,what will be the new velocity in $km/h$?

$A$ bomb at rest explodes into $3$ parts of the same mass. The momentum of two parts is $-3 p \hat{i}$ and $2 p \hat{j}$ respectively. The magnitude of the momentum of the third part is

$A$ spacecraft of mass $M$ moving with velocity $v$ suddenly breaks into two pieces of equal mass $m$. After the explosion,one of the masses $m$ becomes stationary. What is the velocity of the other part of the craft?

$A$ machine gun of mass $10\,kg$ fires $20\,g$ bullets at the rate of $180$ bullets per minute with a speed of $100\,m s^{-1}$ each. The recoil velocity of the gun is $.............\,m/s$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module