As shown in the figure,a small wheel is coaxially connected to a larger wheel of double its radius. The system rotates about a common axis. Strings $A$ and $B$ are attached to the wheels such that they do not slip. If $x$ and $y$ are the distances covered by $A$ and $B$ in the same time interval,then:

$A$ mass $m$ hangs with the help of a string wrapped around a pulley on a frictionless bearing. The pulley has mass $m$ and radius $R$. Assuming the pulley to be a perfect uniform circular disc,the acceleration of the mass $m$,if the string does not slip on the pulley,is

How can one verify that an object is undergoing rotation about a fixed axis?

$A$ ring of mass $m$ can freely slide along the massless curved rod as shown. At the lower most point,the curved path becomes vertical. If the whole system is released from rest,what is the velocity of the ring $(v)$ at the lowermost point just before touching the block $M$ (all surfaces are smooth)?

$A$ uniform disc with mass $M = 4\,kg$ and radius $R = 10\,cm$ is mounted on a fixed horizontal axle as shown in the figure. $A$ block with mass $m = 2\,kg$ hangs from a massless cord that is wrapped around the rim of the disc. During the fall of the block,the cord does not slip and there is no friction at the axle. The tension in the cord is . . . . . . $N$. (Take $g = 10\,m/s^2$)

$A$ uniformly thick wheel with moment of inertia $I$ and radius $R$ is free to rotate about its centre of mass (see fig). $A$ massless string is wrapped over its rim and two blocks of masses $m_{1}$ and $m_{2}$ $(m_{1} > m_{2})$ are attached to the ends of the string. The system is released from rest. The angular speed of the wheel when $m_{1}$ descends by a distance $h$ is