A circular disk of moment of inertia $I_t$ is rotating in a horizontal plane, about its symmetry axis, with a constant angular speed $\omega _i$. Another disk of moment of inertia $I_b$ is dropped coaxially onto the rotating disk. Initially the second disk has zero angular speed. Eventually both the disks rotate with a constant angular speed $\omega _f$. The energy lost by the initially rotating disc to friction is
A circular disk of moment of inertia $I_t$ is rotating in a horizontal plane, about its symmetry axis, with a constant angular speed $\omega _i$. Another disk of moment of inertia $I_b$ is dropped coaxially onto the rotating disk. Initially the second disk has zero angular speed. Eventually both the disks rotate with a constant angular speed $\omega _f$. The energy lost by the initially rotating disc to friction is
- A
$\frac{1}{2}\frac{{{I_b}{I_t}}}{{({I_t} + {I_b})}}\omega _i^2$
- B
$\frac{1}{2}\frac{{I_b^2}}{{({I_t} + {I_b})}}\omega _i^2$
- C
$\frac{1}{2}\frac{{I_t^2}}{{({I_t} + {I_b})}}\omega _i^2$
- D
$\frac{{{I_b} - {I_t}}}{{({I_t} + {I_b})}}\omega _i^2$
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