A clock has $75 \mathrm{~cm}, 60 \mathrm{~cm}$ long second hand and minute hand respectively. In $30$ minutes duration the tip of second hand will travel $x$ distance more than the tip of minute hand. The value of $x$ in meter is nearly (Take $\pi=3.14$ ) :

A proton of mass $ 1.6  \times 10^{-27} kg$ goes round in a circular orbit of radius $0.10\, m$ under a centripetal force of $4  \times 10^{-13}\, N$. then the frequency of revolution of the proton is about 

A particle, moving with uniform speed $v$, changes its direction by angle $\theta$ in time $t$. Magnitude of its average acceleration during this time is

Roads are banked on curves so that

An electric fan has blades of length $30 \,cm$ as measured from the axis of rotation. If the fan is rotating at $1200\,$ r.p.m. , the acceleration of a point on the tip of the blade is about ..........  $m/sec^2$

A string of length $L$ is fixed at one end and carries a mass $M$ at the other end. The string makes $2/\pi$ revolutions per second around the vertical axis through the fixed end as shown in the figure, then tension in the string is