In pure translational motion,the velocity of every particle of a body at any instant is what? Equal or unequal?

$A$ $5\, m$ long pole of $3\, kg$ mass is placed against a smooth vertical wall as shown in the figure. Under equilibrium condition,if the pole makes an angle of $37^{\circ}$ with the horizontal,the frictional force between the pole and the horizontal surface is

$A$ rigid body is rotating with angular velocity $\omega$ about an axis of rotation. Let $v$ be the linear velocity of a particle which is at a perpendicular distance $r$ from the axis of rotation. Then the relation $v = r \omega$ implies that

$A$ rod of mass $m$ and length $l$ is rotated about one of its ends with an angular velocity $\omega$. What is the tension in the rod at a distance $x$ from the axis of rotation?

One end of a rod of length $L$ is on a horizontal plane. It is inclined at an angle $\alpha$ to the horizontal plane. When released,its angular velocity after coming to the horizontal plane is:

$A$ hemisphere of radius $R$ and mass $4m$ is free to slide with its base on a smooth horizontal table. $A$ particle of mass $m$ is placed on the top of the hemisphere. The angular velocity of the particle relative to the hemisphere at an angular displacement $\theta$ when the velocity of the hemisphere is $v$ is: