For a particle in circular motion the centripetal acceleration is

A student skates up a ramp that makes an angle $30^{\circ}$ with the horizontal. $He /$ she starts (as shown in the figure) at the bottom of the ramp with speed $v_0$ and wants to turn around over a semicircular path xyz of radius $R$ during which he/she reaches a maximum height $h$ (at point y) from the ground as shown in the figure. Assume that the energy loss is negligible and the force required for this turn at the highest point is provided by his/her weight only. Then ( $g$ is the acceleration due to gravity)

$(A)$ $v_0^2-2 g h=\frac{1}{2} g R$

$(B)$ $v_0^2-2 g h=\frac{\sqrt{3}}{2} g R$

$(C)$ the centripetal force required at points $x$ and $z$ is zero

$(D)$ the centripetal force required is maximum at points $x$ and $z$

Consider the two statements related to circular motion in usual notations

$A$. In uniform circular motion $\vec{\omega}, \vec{v}$ and $\vec{a}$ are always mutually perpendicular

$B$. In non-uniform circular motion, $\vec{\omega}, \vec{v}$ and $\vec{a}$ are always mutually perpendicular

The linear speed of the tip of seconds hand of a wall clock is $1.05\,cm\,s^{-1}.$ The length of the seconds hand is nearly  ........ $cm$

A body is whirled in a horizontal circle of radius $20 \,cm$. It has angular velocity of $10\, rad/s$. What is its linear velocity at any point on circular path ....... $m/s$

A car changes speed from $18\,km/h$ to $36\,km/h$ in $5\,s$. The diameter of its wheel is $0.8\,m$ . The angular acceleration of the wheel is ........ $rad/s^2$