A tachometer is a device to measure

A particle is acted upon by a force of constant magnitude which is always perpendicular to the velocity of the particle. The motion of the particle takes place in a plane. It follows that  

For particle $P$ revolving round the centre $O$ with radius of circular path $r$ and angular velocity $\omega$, as shown in below figure, the projection of $OP$ on the $x$-axis at time $t$ is $.................$.

If ${a_r}$ and ${a_t}$represent radial and tangential accelerations, the motion of a particle will be uniformly circular if

The work done on a particle of mass $m$ by a force, $k\left[\frac{x}{\left(x^2+y^2\right)^{3 / 2}} \hat{i}+\frac{y}{\left(x^2+y^2\right)^{3 / 2}} \hat{j}\right]$ ( $K$ being a constant of appropriate dimensions), when the particle is taken from the point $(a, 0)$ to the point $(0, a )$ along a circular path of radius a about the origin in the $x$-y plane is :

A particle moves in $x-y$ plane according to rule $x = {\rm{asin}}\omega t$ and $\;y = {\rm{acos}}\omega t$. The particle follows