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)

$A$ dumbbell is placed on a frictionless horizontal table. Sphere $A$ is attached to a frictionless pivot so that $B$ can be made to rotate about $A$ with constant angular velocity. If $B$ (mass $2M$) makes one revolution in period $P$,the tension in the rod (length $d$) is

$A$ vehicle is moving on a track with constant speed as shown in the figure. The apparent weight of the vehicle is:

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

$A$ train is moving with a speed of $12 \,m/s$ on rails which are $1.5 \,m$ apart. To negotiate a curve of radius $400 \,m$, the height by which the outer rail should be raised with respect to the inner rail is (Given, $g = 10 \,m/s^2$): (in $\,cm$)

Two particles of mass $m$ are constrained to move along two horizontal frictionless rails that make an angle $2\theta$ with respect to each other. They are connected by a spring with spring constant $k$. The angular frequency of small oscillations for the motion where the two masses always stay at the same distance from the meeting point of the rails is: