Explain the conservation of linear momentum for the radioactive decay of radium nucleus.
A radium nucleus disintegrates into a nucleus of radon and an $\alpha$-particle. The forces leading to the decay are internal to the system and the external forces on the system are negligible.
The total linear momentum of the system is the same before and after decay, according to law of conservation of linear momentum.
For this, the radon nucleus and the $\alpha$-particle, move in different directions along the same path along which the original decaying radium nucleus was moving it is shown in figure $(a)$.
If we observe decay of the nucleus from the frame of reference whose centre of mass is at rest, the produced particles move near and opposite to each other such that their centre of mass is at rest. It is shown in figure $(b)$.
In many problems on the system of particles as in the above radioactive decay problem, it is convenient to work in the centre of mass frame rather than in the laboratory frame of reference.
A body of mass $0.25 \,kg$ is projected with muzzle velocity $100\,m{s^{ - 1}}$ from a tank of mass $100\, kg$. What is the recoil velocity of the tank ........ $ms^{-1}$
A bomb is projected with $200\,m/s$ at an angle $60^o$ with horizontal. At the highest point, it explodes into three particles of equal masses. One goes vertically upward with velocity $100\,m/sec$, second particle goes vertically downward with the same velocity as the first. Then what is the velocity of the third one-
Why law of conservation of linear momentum is universal and fundamental law ?
Explain conservation of linear momentum by suitable example.
An isolated rail car originally moving with speed $v_0$ on a straight, frictionles, level track contains a large amount of sand. $A$ release valve on the bottom of the car malfunctions, and sand begins to pour out straight down relative to the rail car. Is momentum conserved in this process?