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A ball of mass m collides with a stationary wedge of mass M, perpendicular to its inclined face, inclined at an angle as shown in the figure. If the coefficient of restitution between the wedge and ball is e, calculate the ratio of modulus of velocity of the ball immediately after and before collision. Also calculate the velocity of wedge just after collision.

Answer» <html><body><p><br/></p>Solution :Let velocity of wedge after colision be `v_(2)` and that of ball be `v_(<a href="https://interviewquestions.tuteehub.com/tag/1-256655" style="font-weight:bold;" target="_blank" title="Click to know more about 1">1</a>)` . We can show that `v_(1)<a href="https://interviewquestions.tuteehub.com/tag/ltu-3715552" style="font-weight:bold;" target="_blank" title="Click to know more about LTU">LTU</a>` , because otherwise final `KE` would be greater than initial `KE` which is not possible `v_(1)` will be perpendicular to wedge surface. <br/> From Newoton's experimental law: <br/> ` e=(v_(2)sinalpha-(-v_(1)))/uimpliesv_(2)=(eu-v_(1))/(sinalpha)`.....i <br/> <img src="https://d10lpgp6xz60nq.cloudfront.net/physics_images/BMS_VOL2_C01_E01_081_S01.png" width="80%"/> <br/> Conservastion of linear mometum along `x`-<a href="https://interviewquestions.tuteehub.com/tag/axis-889931" style="font-weight:bold;" target="_blank" title="Click to know more about AXIS">AXIS</a>. <br/> `musinalpha=-mv_(1)sinalpha+Mv_(2)` ...........ii <br/> From i and ii `v_(1)/u=(Me-msin^(2)alpha)/(M+sin^(2)alpha)` <br/> Put the <a href="https://interviewquestions.tuteehub.com/tag/value-1442530" style="font-weight:bold;" target="_blank" title="Click to know more about VALUE">VALUE</a> of `v_(1)` in eqn i to get `v_(2)` <br/> `v_(2)=1/(sinalpha)[eu-((Me-msin^(2)alpha)u)/(M+msin^(2)alpha)]=(musinalpha(e+1))/(M+msin^(2)alpha)`</body></html>


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