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Q.294. There is a narrow beam of negative pions with kinetic energy T equal to the rest energy of these particles. Find the ratio of fluxes at the sections of the beam separated by a distance l = = 20 m. The proper mean lifetime of these pions is ζo= 25.5 ns. 

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Here
so the life time of the pion in the laboratory frame is

The law of radioactive decay implies that the flux decrease by the factor.

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10.25. MOLECULAR THEORY OF SURFACE TENSION The phenomenon of surface tension has been explained in terms of molecular theory, according to which every liquid is made up of a large number of molecules. Let be the surface film of a liquid at rest in a trough. where molecular range, Fig. 10,19. Consider three molecules . and . is well inside the liquid. lies in the surface film and lies at the top of the surface film. Curcles around A. B. Crepresent their spheres of influence. The molecules in the upper half of sphere of influence exert a resultant upward force of cohesion and those in lower half of sphere of influence exert a resultant downward force of cohesion, on the molecule at the centre. Since the sphere of influence of molecule A lies inside the liquid, the number of molecules in the upper. half of sphere of influence is the same as that in its lower balf. Therefore, the resultant upward fonoe of cohesion on molecule is balanced by the resultant downward force of cohesion on it. Hence the net force of. cohrsion on the molecule is zero. The molecule has negative potential energy. It is same for all other molecules of liquid at a grven tempenafure. Since the sphere of influence of molecule lies partly outside the liquid, the number of molecules attracting molecule downwards is more than the number of molecules attracting it upwards. Therefore. there is a resuliam downward force of cohesion acting on molecule . Since the sphere of influence of molecule lies half outside the liquid. hence number of molecules in the lower half of sphere of influence of , attracting it downwards is very large as compared to number of molecules (only gas or vapour molecules) in the upper half of its sphere of influence attracting it upwards. Therefore, there is a maximum resultant downward force acting on molecule . From above, we conclude that no resultant force acts on a molecule, so long it lies below the surface film. But for all those molecules lying in the surface film, a resultant downward force of cohesion acts whach increases as we move from the bottom (NM) of the surface film to its top . This means, to take a molecule into the surface film from anywhere below it, some work is to be done against the downward force of cohesion. This work done appears as additional potential energy of the molecule. Thus all the molecules in the surface film possess additional potential energy, which shows that the surface film has additional potential energy The greater is the number of molecules in the surface film, the larger is the additional potential energy of the surface film. We know that every system, in a state of stable equilibrium has minimum potential energy. In order io attain the stable equilibrium, the surface film also tends to have the minimum additional potential eneri. which will be so if number of molecules in the surface film are minimum. For this, the surface film shoill have minimum volume, which would be so, if the surface film has least surface area, as its thickness is fixed
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Question Text
Q.294. There is a narrow beam of negative pions with kinetic energy T equal to the rest energy of these particles. Find the ratio of fluxes at the sections of the beam separated by a distance l = = 20 m. The proper mean lifetime of these pions is ζo= 25.5 ns. 
TopicNuclei
SubjectPhysics
ClassClass 12
Answer TypeText solution:1
Upvotes14