Given structures are lying in vertical plane and are hinged at x. Every structure is made up of two identical rods with mass M & length L each. Initially all are at rest and released. Initially in every case, one of the rods of the structure is vertical and the other horizontal

Options

A. `{:(P,Q,R,S),(2,3,4,1):}`
B. `{:(P,Q,R,S),(1,4,2,3):}`
C. `{:(P,Q,R,S),(3,2,4,1):}`
D. `{:(P,Q,R,S),(2,3,1,2):}`

Answer

D

Explanation

Initially, As the acceleration of COM is not vertical in all the cases so, hinge force can not be vertical
for `(2),alpha_(x)=(pi)/(I)=(3mgL)/(2.2mL^(2))=(3g)/(4L)`
When K.E. becomes maximum the COM of the structure is lowest.
`K.E._(Max) =2Mg [3+sqrt(10)/(4)]L`
Angle turned for `(1)`
`(pi)/(2)+ tan_(-1) ((1)/(3))`
Moment of inertia
`B rarr(2ML_(2))/(3)`