A particle is in uniform circular motion, then its velocity is perpendicular to

A bob is whirled in a horizontal plane by means of a string with an initial speed of $\omega \mathrm{rpm}$. The tension in the string is $T$. If speed becomes $2 \omega$ while keeping the same radius, the tension in the string becomes:

Certain neutron stars are believed to be rotating at about $1\,rev/\sec $. If such a star has a radius of $ 20\, km$, the acceleration of an object on the equator of the star will be

The angular speed of seconds needle in a mechanical watch is

A particle at a distance of $1 m$ from the origin starts moving, such that $d r / d \theta=r$, where $r$ and $\theta$ are polar co-ordinates. Then, the angle between resultant velocity and tangential velocity is

A boy ties a stone of mass $100 \,g$ to the end of a $2$ $m$ long string and whirls it around in a horizontal plane. The string can withstand the maximum tension of $80 \,N$. If the maximum speed with which the stone can revolve is $\frac{ K }{\pi} rev$. / $min$. The value of $K$ is (Assume the string is massless and unstretchable)