In the given figure,the linear acceleration of the solid cylinder of mass $m_2$ is $a_2$. Then,its angular acceleration $\alpha_2$ is (given that there is no slipping):

$A$ 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

$A$ uniform disc of radius $R$ and mass $M$ is free to rotate only about its axis. $A$ string is wrapped over its rim and a body of mass $m$ is tied to the free end of the string as shown in the figure. The body is released from rest. Then the acceleration of the body is

$A$ wheel starting from rest gains an angular velocity of $10 \ rad/s$ after being uniformly accelerated for $5 \ s$. The total angle through which it has turned is

$A$ solid cylinder of mass $M$ and radius $R$ is placed in a horizontal position. Two strings are wrapped around the cylinder. Find the tension in the strings and the acceleration of the cylinder as the strings unwind.

$A$ flywheel is accelerated uniformly from rest and rotates through $5 \, rad$ in the first second. The angle rotated by the flywheel in the next second will be ......... $rad$.