A disc of mass $3 \,kg$ rolls down an inclined plane of height $5 \,m$. The translational kinetic energy of the disc on reaching the bottom of the inclined plane is .......... $J$

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

A spherical solid ball of $10\,kg$ mass and radius $3\,cm$ is rotating about an axis passing through its centre with an angular velocity of $50\,radian/s$ the kinetic energy of rotation is ....... $J.$

A uniform sphere of mass $500\; g$ rolls without slipping on a plane horizontal surface with its centre moving at a speed of $5.00\; \mathrm{cm} / \mathrm{s}$. Its kinetic energy is

$A$ ring of mass $m$ and radius $R$ has three particles attached to the ring as shown in the figure. The centre of the ring has a speed $v_0$. The kinetic energy of the system is: (Slipping is absent)

A circular disc of moment of inertia $I_t$, is rotating in a horizontal plane, about its symmetry axis, with a constant angular speed $\omega_i$ . Another disc of moment of inertia $l_b$ is dropped coaxially onto the rotating disc. Initially the second disc has zero angular speed. Eventually both the discs rotate with a constant angular speed $\omega_f$. The energy lost by the initially rotating disc to friction is