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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)`.

Text Solution

Verified by Experts

Applying energy conservation
`mg(h + x) = (1)/(2) (k_(1)k_(2))/(k_(1) + k_(2))x^(2)`
where `k_(1) = (A_(1)Y_(1))/(l_(1)) , k_(1) = (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_(2)l_(1))`
`k_(eq)x^(2) - 2mgx - mgh = 0`
`x = (2mg+- sqrt(4m^(2)g^(2) + 8mghk_(eq)))/(2k_(eq)), x_(mass) = (mg)/(k_(eq)) + sqrt((m^(2)g^(2))/(k_(eq)^(2)) + (2mgh)/(k_(eq)))`
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