1)

A disc of the moment of interia 'l1' is rotating in a horizontal plane about an axis passing through a centre and perpendicular to its plane with constant angular speed 'ω1'. Another disc of moment of interia 'l2'  having zero angular speed is placed co-axially on a rotating disc . Now, both the discs are rotating with constant angular speed 'ω2 . The energy lost by the initial rotating disc is 


A) 12[l1+l2l1l2]ω21

B) 12[l1l2l1l2]ω21

C) 12[l1l2l1l2]ω21

D) 12[l1l2l1+l2]ω21

Answer:

Option D

Explanation:

Net  external torque  on the system is zero. Therefore, angular momentum of  the system will remain  same.

    l1ω1=(l1+l2)ω2

ω2ω1=l1l1+l2 .....(i)

 The energy lost . E1E2

=12l1ω2112(l1+l2)ω22

=12ω21[l1(l1+l2)ω22ω21]

 =12ω21[l1(l1+l2)l21(l1+l2)2]

                              [ Eq.(i)]

 =12ω21[l21+l1l2l21(l1+l2)]

  =12[l1l2l1+l2]ω21