A solid cylinder and a solid sphere, having same mass M and radius R, roll down the same inclined plane from top without slipping. They start from rest. The ratio of velocity of the solid cylinder to that of the solid sphere, with which they the ground will be:

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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