A uniform L shaped rigid body AOB of mass 1 kg , where AO = OB = 10 m and ∠ AOB is a right angle, is hinged to a smooth joint at Point A of the body and can swing freely in a vertical plane. Initial

Question

A uniform L shaped rigid body AOB of mass 1 kg , where AO = OB = 10 ​ m and ∠ AOB is a right angle, is hinged to a smooth joint at Point A of the body and can swing freely in a vertical plane. Initially, the body is released from rest with AB horizontal. The maximum kinetic energy of the body is K Joule. The value of ( 5 5 ​ + 25 ) K ​ is :-

TestHub · Accepted Answer

The centre of mass of the L-shaped body is at distance $\frac{5}{2}$ m from A, and with AB horizontal it sits $\frac{10}{2 2}$ m below A's level; the KE is maximum when the COM hangs directly below A.

$K = m g (\frac{5}{2} + \frac{10}{2 2}) = 10 (\frac{5}{2} + \frac{5}{2}) = 25 + 55$ J, so $\frac{K}{5 5 + 25} = 1$ .

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