Three point particles of masses $10\mathrm{k}\mathrm{g},1.5\mathrm{k}\mathrm{g}$ $$ and $$ $2.5\mathrm{k}\mathrm{g}$ are placed at there corners of a right angle triangle of sides $4.0\mathrm{c}\mathrm{m},3.0;\mathrm{c}\mathrm{m}$ $$ and $$ $5.0\mathrm{c}\mathrm{m}$ as shown in the figure. The centre of mass of the system is at a point:

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 :
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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:
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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 :

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