Correct Answer - C
During collision, the torque of the system about P will be
zero because the only force acting on the system is through
P(namely weight of rods/mass m/reaction at P)
`Given: l =0.6m`
m_A 0.01kg`
`m_B = 0.02kg`
`m= 0.05kg`
since `tau = (dt)/(dt) and tau = 0`
`rArr L is constant.`
Angular momentum before collision `=mvxx2l ..(i)`
Angular momentum after collision `=iomega ..(ii)`
Where I is the moment of inertia of the system after collision
about P and `omega` is the angular velocity of the system. `M.I. about P:I_1 = M.I. of mass m`
`I_2 = M.I. of rod m_A`
`I_3 = M.I. of rod m_B`
`I=I_1+I_2+I_3`
`=[m(2l)^2 + {m_A((l^2)/(12)) + ((l)/(2))^2} + {m_B((l^2)/(12)) + ((l)/(2)+l)^2}]`
`=[4ml^2 + m_A((l^2)/(12)+(l^2)/(4)) + m_B ((l^2)/(12)+(9l^2)/(4))]`
`=[4ml^2 + (1)/(3)m_Al^2 +(7)/(3)mBl^2] = 0.09kgm^2`
Frm (i) and (ii)
`I oemga = mvxx2l`
`rArr omega = (mvxx2l)/(I) =(0.05xxvxx2xx0.6)/(0.09) = 0.67v`
Applying conservation of mechanical energy after collision.
(Using the concept of mass)
Loss of K.E. = Gain in P. E.
`(1)/(2)I omega^2 = mg(2l)+m_A((l)/(2))g +m_Bg((3l)/(2))`
`rArr (1)/(2)xx0.09xx(0.67v)^2`
`=[0.05xx2+0.01xx(1)/(2)xx(3)/(2)]xx9.8xx0.6`
`rArr v = 6.3m//s`