A disc of radius R is rotating with an angular speed ωo about a horizontal axis. It is placed on a horizontal table. The coefficient of kinetic friction is µk.

(a) What was the velocity of its centre of mass before being brought in contact with the table?

(b) What happens to the linear velocity of a point on its rim when placed in contact with the table? (c) What happens to the linear speed of the centre of mass when disc is placed in contact with the table?

(d) Which force is responsible for the effects in (b) and (c).

(e) What condition should be satisfied for rolling to begin?

(f) Calculate the time taken for the rolling to begin.

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]-->