A particle of mass 4, m which is at rest expl | vedclass

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

Question

(C) Initially,the particle is at rest,so the initial momentum is $0$. By the law of conservation of linear momentum,the final momentum must also be $0

Vedclass · Accepted Answer

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

Vedclass · Answer

(C) Initially,the particle is at rest,so the initial momentum is $0$. By the law of conservation of linear momentum,the final momentum must also be $0$.Let the two fragments of mass $m$ move in the $x$ and $y$ directions with velocity $v$. Their momenta are $\vec{p}_1 = mv \hat{i}$ and $\vec{p}_2 = mv \hat{j}$.The resultant momentum of these two fragments is $\vec{p}_{12} = \sqrt{(mv)^2 + (mv)^2} = \sqrt{2} mv$.To conserve momentum,the third fragment of mass $M_3 = 4m - m - m = 2m$ must have a momentum $\vec{p}_3$ such that $\vec{p}_1 + \vec{p}_2 + \vec{p}_3 = 0$,which means $\vec{p}_3 = -(\vec{p}_1 + \vec{p}_2)$.The magnitude of the momentum of the third fragment is $p_3 = \sqrt{2} mv$.Since $p_3 = M_3 v_3$,we have $2m v_3 = \sqrt{2} mv$,which gives $v_3 = \frac{v}{\sqrt{2}}$.The total energy released is equal to the final kinetic energy of the fragments:$KE = \frac{1}{2} m v^2 + \frac{1}{2} m v^2 + \frac{1}{2} (2m) v_3^2$$KE = mv^2 + m \left(\frac{v}{\sqrt{2}}\right)^2 = mv^2 + m \left(\frac{v^2}{2}\right) = \frac{3}{2} mv^2$.

$A$ particle of mass $4\, m$ which is at rest explodes into three fragments. Two of the fragments,each of mass $m$,are found to move with a speed $v$ each in perpendicular directions. The total energy released in the process will be

Similar Questions

From a stationary tank of mass $125000 \ lb$,a small shell of mass $25 \ lb$ is fired with a muzzle velocity of $1000 \ ft/sec$. The tank recoils with a velocity of ............ $ft/sec$.

Neglecting friction,if a person sitting at the back of a motorcycle moving on a straight path falls off while the motorcycle is in motion,will the velocity of the motorcycle increase or decrease? Why?

Why is the law of conservation of linear momentum considered fundamental and universal?

$A$ ball of mass $m$ is moving towards a wall with velocity $v$ at an angle $\theta$ with the normal to the wall, as shown in the diagram. In which direction is its linear momentum conserved?

$A$ bullet is fired from a rifle. If the rifle recoils freely,then the kinetic energy of the rifle is

Vedclass Test Series

Exam Paper Generator

Online Exam Module