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neeraj_agarwal_1990 (887)

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Consider a collection of large no. of particles each with speed 'v'. The direction of velocity is randomly distributed in the collection. The magnitude of relative velocity between a a pair of particles averaged over all the pairs is:

(a)  zero  

(b) greater than v

(c) less than v

(d) v



[ans :- (b)]
    
neeraj_agarwal_1990 (887)

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Why is anybody not replying???
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edison (5140)

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Well the collection of large no. of particles having speed of each particle 'v' is practically not possible and if instantaneously if it is made so somehow than due to scattering (elastic and inelastic) and collision the situation will immedeatly chang.
 
Moreover, in the given case the average relative velocity of these particles will be zero as the distribution is random.
 
As far as the selection of pair of two particles for the purpose of magnitude of relative velocity between a a pair of particles is concerned then the solution or answer all depends on the pair of particles selected
This is because for the given pair the direction of velocities may be opposite or in the same direction or may subtend some angle.
 
So it is absurd to talk about relative velocities but ofcourse we can comment something on relative speed.
 
And if it is relative speed then definitely option is (b)

The Scientist does not study nature because it is useful; he studies it because he delights in it, & he delights in it because it is beautiful. If nature were not beautiful, it would not be worth knowing, life would not be worth living. Ofcourse I do not here speak of that beauty that strikes the senses, the beauty of qualities & appearances; not that I undervalue such beauty, far from it, but it has nothing to do with science; I mean that profounder beauty which comes from the harmoniuos order of the parts, & which a pure intelligence can grasp.
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