$A$ particle starts from the point $(0\,m, 8\,m)$ and moves with a uniform velocity of $3\, \hat{i} \,m/s$. After $5\,s$,the angular velocity of the particle about the origin will be:

$A$ hinged construction consists of three rhombs with the side ratio $5:3:2$. Vertex $A_3$ moves in the horizontal direction at a velocity $v$. The velocity of $A_2$ is ....... $V$.

$A$ uniform metallic rod rotates about its perpendicular bisector with constant angular speed. If it is heated uniformly to raise its temperature slightly,what happens to its speed of rotation?

$A$ particle of mass $m$ moving horizontally with velocity $v_0$ strikes a smooth wedge of mass $M$,as shown in the figure. After the collision,the ball starts moving up the inclined face of the wedge and rises to a height $h$. When the particle has risen to a height $h$ on the wedge,choose the correct alternative$(s)$.

Find the increase in the moment of inertia $I$ of a uniform rod (coefficient of linear expansion $\alpha$) about its perpendicular bisector when its temperature is slightly increased by $\Delta T$.

$A$ disc having velocity $v_0$ and angular speed $\omega_0$ in the anticlockwise direction is placed on a rough plank. Initially,the plank is at rest. (Assume the length of the plank is very large). Choose the $INCORRECT$ option.