A spherical bob hangs from a light inextensible string and moves in a horizontal circle with string making angle $\theta$ with the vertical. The length $l$ of the string is then very slowly increased so that the motion is circular at all times to a good approximation. If $h$ is the height from center of the circle to the pivot and $r$ is the radius of the circle then $h\propto r^a$. The value of $a$ is

Two stones of masses $m$ and $2m$ are whirled in horizontal circles, the heavier one in radius $\frac{r}{2}$ and the lighter one in radius $r$. The tangential speed of lighter stone is $n$ times that of the tangential speed of the heavier stone. They are reported to experience the same centripetal force. The value of $n$ is, 

In the given figure, $a=15 \mathrm{m} {\mathrm{s}}^{-2}$ represents the total acceleration of a particle moving in the clockwise direction in a circle of the radius $R=2.5 \mathrm{m}$at a given instant of time. The speed of the particle is

If the kinetic energy of a particle of mass $m,$ performing uniform circular motion in a circle of radius $r,$ is $E,$ find the acceleration of the particle.