A particle $P$ is moving in a circle of radius $'a'$ with a uniform speed $v$. $C$ is the centre of the circle and $AB$ is a diameter. When passing through $B$ the angular velocity of $P$ about $A$ and $C$ are in the ratio

A cylindrical vessel partially filled with water is rotated about its vertical central axis. It’s surface will

$Assertion$ : When a particle moves in a circle with a uniform speed, its velocity and acceleration both changes.

$Reason$ : The centripetal acceleration in circular motion is dependent on angular velocity of the body.

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 conical pendulum of length $1\,m$ makes an angle $\theta \, = 45^o$ w.r.t. $Z-$ axis and moves in a circle in the $XY$ plane.The radius of the circle is $0.4\, m$ and its centre is vertically below $O$. The speed of the pendulum, in its circular path, will be ..... $m/s$ (Take $g\, = 10\, ms^{-2}$)

A particle is moving in a circle of radius $r$ having centre at $O$, with a constant speed $v$. The magnitude of change in velocity in moving from $A$ to $B$ is