If the net force acting on the system of particles is zero, then which of the following may vary?

Consider a semicircular ring of radius $R$. Its linear mass density varies as $\lambda ={\lambda }_0\sin \theta$. Locate its centre of mass.

The block wedge system shown in the figure is released from rest. All the surfaces are smooth. Find the speed of the wedge when the speed of the block w.r.t. wedge is $v$.

A block of mass $\mathrm{m}$ is moving with speed $v$ on a wedge of mass $M$ which is placed upon a horizontal surface. Track $AB$ is a circular track of radius $R$. What is the minimum speed $v$, so that the block reaches point $A$ (All surfaces are frictionless)?

Two blocks $A$ and $B$ are connected by a spring of stiffness $200 \mathrm{N} {\mathrm{m}}^{-1}$ and placed on a smooth horizontal surface. Initially the spring has its equilibrium length. The indicated velocities are imparted to $A$ and $B$. The maximum extension of the spring will be

A bead can slide on a smooth straight wire and a particle of mass $\mathrm{m}$ attached to the bead by a light string of length $L$. The particle is held in contact with the wire and with the string taut and is then let fall. If the bead has mass $2\mathrm{m}$ then when the string makes an angle $\theta$ with the wire, the bead will have slipped a distance