$A$ plank is resting on a horizontal ground in the northern hemisphere of the earth at a $45^{\circ}$ latitude. Let the angular speed of the earth be $\omega$ and its radius $r_e$. The magnitude of the frictional force on the plank will be

$A$ gramophone record is rotating with an angular velocity $\omega$. $A$ coin is placed at a distance $r$ from the center of the record. The coefficient of static friction is $\mu$. The coin will revolve with the record if .......

$A$ car sometimes overturns while taking a turn. When it overturns,which wheel leaves the ground first?

$A$ cyclist moves on a circular track of radius $100 \ m$. If the coefficient of friction is $0.2$,then the maximum velocity with which the cyclist can take the turn while leaning inwards is ...... $m/s$.

$A$ large drum having radius $R$ is spinning around its axis with angular velocity $\omega$,as shown in the figure. The minimum value of $\omega$ so that a body of mass $M$ remains stuck to the inner wall of the drum,taking the coefficient of friction between the drum surface and mass $M$ as $\mu$,is:

$A$ small mass $m$ rests at the edge of a horizontal disc of radius $R$. The coefficient of static friction between the mass and the disc is $\mu$. The disc is rotated about its axis at an angular velocity such that the mass slides off the disc and lands on the floor $h$ meters below. What was its horizontal distance of travel from the point it left the disc?