Between the hour hand of a clock and the rotation of the Earth about its own axis,which has a lower angular speed?

$A$ uniform rod of length $l$ is being rotated in a horizontal plane with a constant angular speed $\omega$ about an axis passing through one of its ends. If the tension generated in the rod due to rotation is $T(x)$ at a distance $x$ from the axis,then which of the following graphs depicts it most closely?

The potential energy of a particle of mass $m$ at a distance $r$ from a fixed point $O$ is given by $V(r) = kr^2 / 2$,where $k$ is a positive constant of appropriate dimensions. This particle is moving in a circular orbit of radius $R$ about the point $O$. If $v$ is the speed of the particle and $L$ is the magnitude of its angular momentum about $O$,which of the following statements is (are) true?
$(A)$ $v = \sqrt{\frac{k}{2m}} R$
$(B)$ $v = \sqrt{\frac{k}{m}} R$
$(C)$ $L = \sqrt{mk} R^2$
$(D)$ $L = \sqrt{\frac{mk}{2}} R^2$

$A$ thin ring of radius $R$ is rotated about its center. Then its radius:

$A$ plank with a uniform sphere placed on it rests on a smooth horizontal plane. The plank is pulled to the right by a constant force $F$. If the sphere does not slip over the plank,which of the following is true?

$A$ door $1.6 \,m$ wide requires a force of $1 \,N$ to be applied at the free end to open or close it. The force that is required at a point $0.4 \,m$ distance from the hinges for opening or closing the door is (in $\,N$)