Two cylindrical hollow drums of radii R and 2R, and of a common height h, are rotating with angular velocities ω (anti-clockwise) and ω (clockwise), respectively. Their axes, fixed are parallel and in a horizontal plane separated by (3 ) R + δ . They are now brought in contact ( 0) δ → .

(a) Show the frictional forces just after contact.

(b) Identify forces and torques external to the system just after contact.

(c) What would be the ratio of final angular velocities when friction ceases

The position vector of 1kg object is $\overrightarrow{r}=\left(3\widehat{i}-\widehat{j}\right)m$ and its velocity $\overrightarrow{v}=\left(3\widehat{j}+\widehat{k}\right)m{s}^{-1}.$ The magnitude of is angular momentum is $\sqrt[]{x}Nm$  where x is________.

Match List – I with List – II

Choose the correct answer from the options given below:

A shell of mass $m$ is at rest initially. It explodes into three fragments having mass in the ratio $2:2:1$ . If the fragments having equal mass fly off along mutually perpendicular directions with speed $v$ , the speed of the third (lighter) fragment is :
<!-- [if !supportLineBreakNewLine]-->
<!--[endif]-->

The angular speed of a fly wheel moving with uniform angular acceleration changes from 1200rpm to 3120 <!-- [if gte msEquation 12]>rpm <!--[endif]--><!--[endif]--> in 16 seconds. The angular acceleration in $\mathrm{r}\mathrm{a}\mathrm{d}/{\mathrm{s}}^2$  is:
<!-- [if !supportLineBreakNewLine]-->
<!--[endif]-->

The ratio of the radius of gyration of a thin uniform disc about an axis passing through its centre and normal to its plane to the radius of gyration of the disc about its diameter is :

<!--[endif]-->