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Two smooth spheres A and B, of equal radius but masses m and M, are free to move on a horizontal table. A is projected with speed u towards B which is at rest. On impact, the line joining their centres is inclined at an angle theta to the velocity of A before impact. If e is the coefficient of restitution between the spheres, find the speed with which B begins to move. If A.s path after impact is perpendicular to its path before impact, show that tan ^(2) theta = (eM-m)/(M +m).

Answer» <html><body><p></p><a href="https://interviewquestions.tuteehub.com/tag/solution-25781" style="font-weight:bold;" target="_blank" title="Click to know more about SOLUTION">SOLUTION</a> :When B is struck by the impulse J, it <a href="https://interviewquestions.tuteehub.com/tag/begins-894562" style="font-weight:bold;" target="_blank" title="Click to know more about BEGINS">BEGINS</a> to <a href="https://interviewquestions.tuteehub.com/tag/move-548879" style="font-weight:bold;" target="_blank" title="Click to know more about MOVE">MOVE</a> in the direction of J as shown in the . Along the line of centres, we apply <br/> (a) Conservation of linerar momentum , i.e., `m u cos theta MV - mv …(1)` <br/> (b) Law of resistution, i.e., `eu cos theta = V +v ...(2)` <br/> Solving <a href="https://interviewquestions.tuteehub.com/tag/eqs-2072581" style="font-weight:bold;" target="_blank" title="Click to know more about EQS">EQS</a>. (1) and (2) we get <br/> `v = ((eM - m) u cos theta )/( (M +m))and V = ((1 + e ) m u cos theta)/( (M + m ))` <br/> Hence, `tan phi= ( u sin theta)/( v ) = ((M + m ) tan theta)/( (e M - n ))` <br/> Butthe paths of A before and after <a href="https://interviewquestions.tuteehub.com/tag/impact-1037617" style="font-weight:bold;" target="_blank" title="Click to know more about IMPACT">IMPACT</a> are at rigth angles, therefore,` cot phi = tan theta.` <br/> Hence, `((eM - m ))/( (M + m ) tan theta ) = tan theta` <br/> `therefore tan ^(2) theta = (eM - m )/( (M + m ))`</body></html>


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