Answer:
Here \[{{m}_{1}}={{m}_{2}}=m,\] \[{{u}_{1}}=\upsilon ,\] \[{{u}_{2}}=-\upsilon \] \[\therefore \] \[{{\upsilon }_{1}}=\frac{({{m}_{1}}-{{m}_{2}}){{\upsilon }_{1}}+2{{m}_{2}}{{u}_{2}}}{{{m}_{1}}+{{m}_{2}}}\] \[=\frac{(m-m)\upsilon +2m(-\upsilon )}{m+m}=-\upsilon \] and \[{{\upsilon }_{2}}=\frac{({{m}_{2}}-{{m}_{1}}){{\upsilon }_{2}}+2{{m}_{1}}{{u}_{1}}}{{{m}_{1}}+{{m}_{2}}}=\frac{(m-m)(-\upsilon )+2m\upsilon }{m+m}=\upsilon \]Hence after collision, the two ball bearings will move with same speeds but their directions of motion are reversed.
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