If a particle moves in a circle describing equal angles in equal times, its velocity vector

A particle is moving on a circular path with constant speed $v$. It moves between two points $A$ and $B$. which subtends an angle $60^{\circ}$ at the centre of circle. The magnitude of change in its velocity and change in magnitude of its velocity during motion from $A$ to $B$ are respectively ..........

“Write equation of centripetal acceleration for uniform circular motion. Obtain this equations in terms of angular velocity $(\omega )$ and frequency  $(v)$ .”

If a body moving in circular path maintains constant speed of $10\,ms^{-1},$ then which of the following correctly describes relation between acceleration and radius ?

A particle of mass $200 \,g$ is moving in a circle of radius $2 \,m$. The particle is just 'looping the loop'. The speed of the particle and the tension in the string at highest point of the circular path are $\left(g=10 \,ms ^{-2}\right)$

Read each statement below carefully and state, with reasons, if it is true or false :

$(a)$ The net acceleration of a particle in circular motion is always along the radius of the circle towards the centre

$(b)$ The velocity vector of a particle at a point is always along the tangent to the path of the particle at that point

$(c)$ The acceleration vector of a particle in uniform circular motion averaged over one cycle is a null vector