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 force $\vec F$ acts on a particle having position vector $\vec r$ (with respect to origin). It produces a torque $\vec \tau $ about origin, choose the correct option

In a bicycle the radius of rear wheel is twice the radius of front wheel. If $r_F$ and $r_r$ are the radius, $v_F$ and $v_r$ are the speeds of top most points of wheel, then

A man of $50\, kg$ mass is standing in a gravity free space at a heigth of $10\,m$ above the floor. He throws a stone of $0.5\, kg$ mass downwards with a speed of $2\,m/s$. When the stone reaches the floor, the distance of the man above the floor will be ........ $m.$

A thin wire of length $l$ and uniform linear mass density of $\rho $ is bent into a circular loop with centre $O$ and radius $r$ as shown in the figure. The moment of inertia of the loop about the axis $XX'$ is

For a rolling body, the velocity of $P_1$ and $P_2$ are ${\vec v_1}$ and ${\vec v_2}$ , respectively