A metre scale is balanced on a knife edge at its centre. When two coins, each of mass 10 g are put one on the top of the other at the 10.0 cm mark the scale is found to be balanced at 40.0 cm mark. The mass of the metre scale is found to be x × 10^-2 kg. The value of x is _________.

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 :

The angular speed of a fly wheel moving with uniform angular acceleration changes from 1200rpm to 3120 in 16 seconds. The angular acceleration in $\mathrm{r}\mathrm{a}\mathrm{d}/{\mathrm{s}}^2$  is:

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 :