A particle of mass m_(1) is projected to the right with speed v_(1) onto a smooth wedge of mass m_(2) which is simulateoulsy projected due the left with a speed v_(2). If the particle attains the highest point of the wedge, find h.

A particle of mass m_(1) is projected to the right with speed v_(1) on

1.	A particle of mass m_(1) is projected to the right with speed v_(1) onto a smooth wedge of mass m_(2) which is simulateoulsy projected due the left with a speed v_(2). If the particle attains the highest point of the wedge, find h.
Answer» <html><body><p></p>Solution :Applying work energy <a href="https://interviewquestions.tuteehub.com/tag/theorem-706777" style="font-weight:bold;" target="_blank" title="Click to know more about THEOREM">THEOREM</a> <br/> `W_("<a href="https://interviewquestions.tuteehub.com/tag/total-711110" style="font-weight:bold;" target="_blank" title="Click to know more about TOTAL">TOTAL</a>")=/_\K_("blocks",cm)+/_\K_(cm)` <br/> As no external forces <a href="https://interviewquestions.tuteehub.com/tag/acting-269" style="font-weight:bold;" target="_blank" title="Click to know more about ACTING">ACTING</a>, the velocity of centre of mass will be constant. Hence `/_\K_(cm)=0` <br/> Hence `W_("total")=/_\K_("blocks",cm)` <br/> `W_("gravity")=[1/2muv_(rel)^(<a href="https://interviewquestions.tuteehub.com/tag/2-283658" style="font-weight:bold;" target="_blank" title="Click to know more about 2">2</a>)]_("final")-[1/2muv_(rel)^(2)]_("initial")` <br/> `-m_(1)gh0-1/2((m_(1)m_(2))/(m_(1)+m_(2)))(v_(1)+v_(2))^(2)` <br/> `-m_(1)gh=-1/2((m_(1)m_(2))/(m_(1)+m_(2)))(v_(1)+v_(2))^(2)` <br/> `h=1/2(m_(2)(v_(1)+v_(2))^(2))/(g(m_(1)+m_(2)))`</body></html>