$A$ dancer moves counterclockwise at a constant speed around the path shown below. The path is such that the lengths of its segments,$PQ, QR, RS$,and $SP$,are equal. Arcs $QR$ and $SP$ are semicircles. Which of the following best represents the magnitude of the dancer's acceleration as a function of time $t$ during one trip around the path,beginning at point $P$?

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)

Two particles of mass $2m$ and $m$ are attached to a light string as shown. The complete system is rotated in a horizontal circle with a constant angular velocity $2\omega$ about an axis passing through point $O$ and perpendicular to the plane of the circle. Find the ratio $T_{OA} / T_{AB}$,where $T_{OA}$ and $T_{AB}$ are the tensions in strings $OA$ and $AB$ respectively.

$A$ coin,placed on a rotating turntable,slips when it is placed at a distance of $9 \, cm$ from the center. If the angular velocity of the turntable is tripled,it will just slip if its distance from the center is ......... $cm$.

$A$ string of length $L$ is fixed at one end and carries a mass of $M$ at the other end. The mass makes $(\frac{3}{\pi})$ rotations per second about the vertical axis passing through the fixed end of the string as shown. The tension in the string is . . . . . . $ML$.

$A$ $500 \, kg$ car takes a round turn of radius $50 \, m$ with a velocity of $36 \, km/hr$. The centripetal force is .......... $N$.