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Hanger is mass less a ball of mass m dro...


Hanger is mass less a ball of mass `m` drops a height `h` which sticks to hanger after striking. Neglect over turning find out the maximum extension in rod. Assuming or id massless let maximum extension be `x_(max)`.

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Applying energy conservation `mg(h+x_(max))=(1)/(2)(k_(1)k_(2))/(k_(1)+k_(2))x^(2)`
where `k_(1)=(A_(1)y_(1))/(l_(1)),k_(2)=(A_(2)y_(2))/(l_(2))&K_(eq)=(A_(1)A_(2)y_(1)y_(2))/(A_(1)y_(1)l_(2)+A_(2)y_(1)l_(1))`
therefore `k_(eq)x_(max)^(2)-2mgx_(max)-2mgh=0`
`x_(max)=(2mg+-sqrt(4m^(2)g^(2)+8mghk_(eq)))/(2k_(eq))=(mg)/(k_(eq))+sqrt((m^(2)g^(2))/(k_(eq)^(2))+(2mgh)/(k_(eq)))`
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