When helical gear $M$ turns as shown,gears $I$ & $H$ turn in the following manner. Which of the following is correct? (Assuming no slipping anywhere)

$A$ particle moves in a horizontal circle on the smooth inner surface of a hemispherical bowl of radius $R$. The plane of motion is at a depth $d$ below the centre of the hemisphere. The speed of the particle is:

$A$ small disc is placed on the top of a smooth hemisphere of radius $R$. The smallest horizontal velocity $V$ that should be imparted to the disc so that it leaves the hemisphere surface immediately is (there is no friction):

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.

$A$ particle of mass $m$ is rotating in a plane in a circular path of radius $r$. Its angular momentum is $L$. The centripetal force acting on the particle is:

$A$ hemispherical bowl of radius $R$ is rotated about its axis of symmetry,which is kept vertical,with angular velocity $\omega$. $A$ small block is kept in the bowl. It remains stationary relative to the bowl surface at a position where the radius makes an angle $\theta$ with the vertical. The friction is absent. The value of $\theta$ is