IIT JEE , AIEEE Forum - Physics , Mechanics

vaibhav_hyderabad1991

2 identical small spheres A n B of mass m each r connectd 2gether by a light n inxtensibl string of length 2L n system is placed at rest on asmooth horizontal surfac ,L distanc a part . d ball B is imparted speed v along +ve x- axis.

1.respectiv speeds of A n B as soon as d string bcoms taught are?

2.vel of com of system aftr d string bcoms taught?

3. if

t is d tym in wich momentum of A changs to a value calculatd in qn 1,then avg force acting on A is?

edison

Here we assume the surface to be frictionless.
Thus the ball B when moves with velocity along +ve x-axis, then it continues to move until the separation becomes 2L and the string becomes fully streched.
1) As masses of the two ball sare same thus ball B stops and its entire momentum is imparted to ball A and ball A srarts to move with velocity v.

Moreover this is in accordance with conservation of momentum as

momentum of ball A before string getting streched + ball B before string is streched = Momentum of ball A after streching + momentum of ball B after string is streched

m.0 + m.v = m.v + m.0

2) Velocity of ceter of mass contimues to be same that is

Vcm = (mv + m.0) / 2m = v/2

3) since time in which momentum of ball changes = t
change in momentum of the ball A = mv - 0 = mv

Then average force = dp/dt = change in momentum/time taken

or force = mv/t

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