An object is moving on a circular track of radius $450\, m$. At some instant, the object is moving at $30\, m/s$ and gaining speed at a uniform rate of $2 m/s^2$. Its acceleration at this instant is nearly  .......... $m/s^2$

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 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  

A particle is tied to $20\, cm$ long string. It performs circular motion in vertical plane. What is the angular speed of particle when the tension in the string at the top is  zero   ......... $rad/sec$

In case of uniform circular motion which of the following physical quantity do not remain constant

A particle moves in a circle of radius $5 \;cm$ with constant speed and time period $0.2 \pi\; sec$. The acceleration of the particle is .... $m/sec^2$