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

    $\frac{{{I_b} - {I_t}}}{{({I_t} + {I_b})}}\omega _i^2$

Similar Questions

Radius of gyration of a body depends on

Two rotating bodies $A$ and $B$ of masses $m$ and $2\,m$ with moments of innertia $I_A$ and $I_B\,(I_B > I_A)$ have equal kinetic energy of rotation. If $L_A$ and $L_B$ be their angular momentum respectively, then

The moment of inertia of a uniform thin rod of length $L$ and mass $M$ about an axis passing through the rod from a point at a distance of $L/3$ from one of its ends perpendicular to the rod is

A rod of length $L$ is held vertically on a smooth horizontal surface. The top end of the rod is given a gentle push. At a certain instant of time, when the rod makes an angle $\theta$ with horizontal the velocity of $COM$ of the rod is $v_0$ . The velocity of the end of the rod in contact with the surface at that instant is 

Two racing cars of masses $m_1$ and $m_2$ are moving in circles of radii $r_1$ and $r_2$ respectively. Their speeds are such that each makes a complete circle in the same time $t$. The ratio of the angular speeds of the first to the second car is