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Asked by adjacentcalliber10 | 18 May, 2019, 13:24: PM
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Figure shows the direction of movement of three spheres immediately after cutting the string that connecting A and B.
Due to Tension force and Electrostatic force Ball A and B moves with velocity vA and vB as shown in figure.
Ball C moves with speed vCy along the direction of y-axis.
 
After resolving velocity vectors and applying momentum conservation,  
 
m × vAy + m × vBy + m × vCy = 0 ...................(1)
 
By symmetry, vAy = vBy = v ,  hence from eqn.(1)  we get  vCy = 2 |v|  ....................(2)
 
Final kinetic energy of system = change in potential energy
 
begin mathsize 12px style 1 half m v squared space plus space 1 half m v squared space plus space 1 half m v subscript c Y end subscript superscript 2 space equals space 2 open square brackets fraction numerator Q squared over denominator 4 πε subscript 0 space 2 straight l end fraction space minus space fraction numerator Q squared over denominator 4 πε subscript 0 space straight l end fraction close square brackets space equals space fraction numerator begin display style Q squared end style over denominator begin display style 4 πε subscript 0 space straight l end style end fraction end style  ........................(3)
using eqn.(2) and after simplification, we get  begin mathsize 12px style v subscript C y end subscript superscript 2 space equals space fraction numerator 4 over denominator 3 m end fraction space fraction numerator Q squared over denominator 4 πε subscript 0 space straight l end fraction end style  ....................(4)
By substituting respective values in eqn.(4) , we get vCy = 2√2 m/s
 
Answered by Thiyagarajan K | 21 May, 2019, 13:37: PM

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