$A$ particle of mass $m$ is rotating in a circular path of radius $r$. Its angular momentum is $L$. The centripetal force acting on it is $F$. The relation between $F$,$L$,$r$,and $m$ 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.

"Momentum and changes in momentum are not always in the same direction." Explain with a suitable example.

$A$ particle rotates in a horizontal circle of radius $r$ in a conical funnel with speed $v$. The inner surface of the funnel is smooth. The height $h$ of the plane of the circle from the vertex of the funnel is (where $g$ is the acceleration due to gravity):

Two particles of the same mass are moving in circular orbits because of a force given by $F(r) = -\frac{16}{r} - r^3$. The first particle is at a distance $r = 1$,and the second is at $r = 4$. The best estimate for the ratio of kinetic energies of the first and the second particle is closest to:

$A$ train is moving towards north. At one place it turns towards north-east,here we observe that