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A,B,C and D are four points on a vertical line such that AB = BC CD. A body is allowed to fall freely from A. Prove that the respective times required by the body to cross the distances AB, BC, CD should be in the ratio 1 : (sqrt(2)-1) : (sqrt(3)-sqrt(2)).

Answer» <html><body><p></p>Solution :Let AB = BC = <a href="https://interviewquestions.tuteehub.com/tag/cd-407381" style="font-weight:bold;" target="_blank" title="Click to know more about CD">CD</a> = x and time taken by the body to cover these distances be`t_(1), t_(2)`and `t_(3)` respectively. <br/> Now, `x = (1)/(2)"gt"_(1)^(2) """or", t_(1) = sqrt((2x)/(<a href="https://interviewquestions.tuteehub.com/tag/g-1003017" style="font-weight:bold;" target="_blank" title="Click to know more about G">G</a>)) ""cdots(1)` <br/>`2x = (1)/(2) g(t_(1)-t_(2))^(2) """or", t_(1)+t_(2)= sqrt((<a href="https://interviewquestions.tuteehub.com/tag/4x-319255" style="font-weight:bold;" target="_blank" title="Click to know more about 4X">4X</a>)/(g)) ""cdots(2)` <br/> `3x = (1)/(2) g(t_(1)+t_(2)+t_(3))^(2)"""or" t_(1)+t_(2)+t_(3)= sqrt((6x)/(g)) "" cdots(3)` <br/> From (1) and (2) we <a href="https://interviewquestions.tuteehub.com/tag/get-11812" style="font-weight:bold;" target="_blank" title="Click to know more about GET">GET</a>, <br/> `t_(2) = sqrt((4x)/(g))-sqrt((2x)/g)=sqrt((2x)/(g))(sqrt(2)-1)` <br/> From (2) and (3) we get , <br/> `t_(3)=sqrt((6x)/(g))-sqrt((4x)/g)=sqrt((2x)/(g))(sqrt(3)-sqrt(2))` <br/> `:. "" t_(1):t_(2):t_(3)=1:(sqrt2-1):(sqrt3-sqrt(2))""`(Proved).</body></html>


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