A) \[\frac{v}{4}\]
B) \[\frac{2v}{3}\]
C) \[\frac{v}{2}\]
D) Zero
Correct Answer: C
Solution :
The initial velocity of first sphere is v While that for second sphere is zero. Suppose, the velocities of first and second spheres after the collision are in uj and u^ respectively. Now, from conservation of momentum \[mv=m{{u}_{1}}+2m{{u}_{2}}\] ?(i) Also, \[e=\frac{\text{velocity}\,\text{of}\,\text{separation}}{\text{velocity}\,\text{of}\,\text{approach}}=\frac{1}{2}\] \[\Rightarrow \] \[\frac{{{u}_{2}}-{{u}_{1}}}{v}=\frac{1}{2}\Rightarrow {{u}_{2}}-{{u}_{1}}=\frac{v}{2}\] ?(ii) From Eqs. (i) and (ii), we get \[{{u}_{1}}=0\]and \[{{u}_{2}}=\frac{v}{2}\]
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