$A$ particle moves in a circular orbit under the action of a central attractive force inversely proportional to the distance $r$. The speed of the particle is

Consider the following statements:
Assertion $(A)$: $A$ cyclist always bends inwards while negotiating a curve.
Reason $(R)$: By bending,he provides the necessary centripetal force by shifting his centre of gravity.

When a disc is rotating with angular velocity $\omega$,a particle situated at a distance of $4 \ cm$ just begins to slip. If the angular velocity is doubled,at what distance will the particle start to slip (in $cm$)?

$A$ car moving at a speed of $72 \; km/hr$ passes through a point $P$ on a curved road with a radius of $10 \; m$. The mass of the car is $500 \; kg$. Find the contact force (normal force) at point $P$ in $kN$. (Take $g = 10 \; m/s^2$)

$A$ mass $m$ is attached to one end of a spring with spring constant $k$ and natural length $l$. The system is rotated in a horizontal plane with an angular velocity $\omega$. What is the extension in the length of the spring?

$A$ uniform chain of mass $m$ and length $L$ is originally placed mid-way on the top of a fixed smooth double-sided wedge. The length of each side of the wedge is $L$. It is then given a slight push. The kinetic energy of the chain when the whole chain has just slid to the left side of the wedge is: