Spring

A block C of mass $m = 2$ kg is placed on a smooth inclined plane with an angle of inclination $\alpha = 30^\circ$. It is attached to a light spring with an unstretched length of $l_0 = 0.2$ m. The other end of the spring is fixed at the top of the incline. When the system is at rest, the spring stretches to a length of $l_1 = 0.25$ m. The entire system (incline and block) rotates about a vertical axis AB as shown. (Use $g = 9.8$ m/s²)

A smooth, thin horizontal rod OA can rotate about a vertical axis MN passing through O. Two identical small objects, each with mass $m_1 = m_2 = m$, are threaded onto the rod. They are connected by two identical light springs, each with spring constant $k$ and natural length $L_0$. The first spring connects the axis at O to mass $m_1$, and the second spring connects mass $m_1$ to mass $m_2$.

A spring with a pointer is hung next to a scale marked in millimeters. When a package of weight $W_1 = 110$ N is hung, the pointer indicates $x_1 = 40$ mm. When a package of weight $W_2 = 240$ N is hung, the pointer indicates $x_2 = 60$ mm. A third package of unknown weight $W$ is hung, and the pointer indicates $x_3 = 30$ mm.