1i asked to arrange not spheres but their velocities..........tell me eureka how can the spheres be arranged....surely they cannot jump over each other.....
all the spheres have equal mass.....and they undergo perfectly elastic collision amongst each other...
they hav velocity whose magnitude is written over the arrows and the direction of their initial velocity is represented by the arrows...
so the question is
after all posssible collisions what is the velocity of ball no.1,2,3,4,5,6,7,8
and also mention the direction of their velocity...
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26 Answers
11brought this one up...bcos jee is near and i feel sumthing like this cud cum up
1but u obtained the final momentum as 35m....that does not give us any hint about the velocities......so whats the use of applying COM here?
24i know we cnat apply eqn after first collison and so on..but i have applied equation on initial and final condition of system..I think we can surely do that..
let me give u an example..
for a two body collision we cant apply conservation of momentum eqnat the instant collision taking place but we apply it at the final condition
here too in final cond is stable equilbrium and no collison taking place..so we can apply it...
1@eureka
u cant apply conservation of momentum principle here because we cant predict what will be the state of the system after 1st collision....
and if we hav to apply we will have to apply it after every collision....
and as we cant predict the number of collisions therefore we cant apply COM....
we can just do this question by imagining the final system.....
24ok....
Since it is elastic collision,
=>Linear Momentum is conserved
=>pi=pf
Now,pi=5m(10)-3m(5)=35m
=>pf=35m
Also we need a stable equilibrium condition so that no collision take place further
=>Relative velocities of balls should be such that the ball following the other should have less velocity
Thats why arranged in such a manner..so that momentum is also conserved along with eqiulibrium cond being attained
Am I right ???or is still something missing ??
Btw from real analysis I got the sitatuion after about 20 collisions...did anyone get that in less collsions ??
62For eureka and others...
Lets see the balls..
One thing: If there is a perfectly elastic collision, then the balls will only change directions. not the magnitude...
Now if the ball which is to the rightmost has a speed lower than the ball whcih is 2nd from the right, then the two balls will collide again (which will mean that the final equilibrium has not been achieved!)
Hence the ball to the right most will have the maximum velocity....
I hope this is a bit more clear ;)
1nishant sir...anant sir...
pls do post a nice elegant solution to this question....
i dont think that others are finding it easy to understand my solution.....
1i have already drawn the final system...........
suppose eureka a person is running with the speed of 12m/sec
can u catch him or collide with him if u run at the speed of 10m/sec...
as the spheres on the extremes have more velocities than the ones next to them therefore....no collsion will occur
24no no...tha increasing order...and decreasign order,I cant understand that concept....
I know I am stretching htis problem a bit too far...but I cant imagine the situtaion u r talking..[2]
1and note that i hav not changed the direction of the velocities
1thats what i hav drawn.........the velocities are written over the spheres...........
24thats what my doubt was..i was confused with what u said...
can u draw the cond of velocities u specified(i.e inc and dec. order too ??)
62Just a hunch!
will it be?
2 2 1 0 1 4 3 2 the first three towards teh left the last 4 towards teh right?
24but u told to arrang spheres on left side in dec order...so how did sphere 3 come in between ??shouldnt it be at extreme ??left end
1this can be generalised for any number of balls.....
we can use this as a trick
just arrange the leftwards velocities in descending order
then comes the 0 velocities
and then arrange the rightwards velocities in ascending order
and whew....u hav the answer both logically and physically correct....
just rember that in headon collision direction of velocities does not change
so the final ans would be-
2,2,1 along left
then 0
and then
1,2,3,4 along right...
now imagine the new system...will the balls ever collide again...?
1no one trying......? its very easy...u just require common sense....
there is always a probability of such questions coming in jee
1doesnt have anything to do with seperation....
we just hav to tell the final velocity.....
1sir u should hav deleted the wrong answer too....it gives a hint as to the direction in which to think
62Arshad I am deleting my explanation and the answer.. and lets keep this for the users to answer...
Indeed this is an awesome questoin :)