$A$ mass $m$ is supported by a massless string wound around a uniform hollow cylinder of mass $m$ and radius $R$. If the string does not slip on the cylinder, then with what acceleration will the mass be released? (Assume $g =$ acceleration due to gravity)

$A$ 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 $g = 10\,m/s^2$)

$A$ uniform rod of mass $m$ and length $l$ is suspended by means of two identical inextensible light strings as shown in the figure. The tension in one string immediately after the other string is cut is . . . . . . . ($g$ is the acceleration due to gravity)

$A$ uniform rod is rotating in a gravity-free region with a certain constant angular velocity $\omega$. The variation of tensile stress $\sigma$ with distance $x$ from the axis of rotation is best represented by which of the following graphs?

$A$ string is wrapped around a disc of mass $M$ and radius $R$ and the free end is fixed to the ceiling. The centre of mass falls down as the disc unwinds the string. The tension in the string is

$A$ rod of length $l$ and mass $m$ lies on a fixed horizontal smooth table. $A$ cord is led through a pulley,and its horizontal part is attached to one end of the rod,while its vertical part is attached to a block of mass $m_1$. Assume the pulley and the cord are ideal. The maximum possible acceleration of the rod's centre of mass $C$ (for all possible values of masses $m$ and $m_1$) at the moment of releasing the block $m_1$ is $\frac{g}{n}$. Find the value of $n$.