Four point mass, each of mass $m$ are connected at a corner of a square of side $\text{'}a\text{'},$ by massless rods as shown in the figure, $x$ and $y$ axis are in the plane of the system and $z$ axis is perpendicular to the plane and passing through the centre of the square.

A force $F$ is applied on the plank such that the hollow hemispherical shell is in equilibrium as shown in the figure. The coefficient of friction $\mu$ is the same between the hemispherical shell and the plank as it is between the plank and the ground. Friction is just sufficient to prevent the slipping (Take $\mathrm{g}=10 \mathrm{m} {\mathrm{s}}^{-2}$ and $m=5 \mathrm{k}\mathrm{g}$). Then

A hexagonal body lies on a horizontal rough surface. A force $F$ acts on the side of a hexagonal body as shown in figure. Choose the correct option(s).

A rod, placed in vertical plane, is being pushed along a smooth horizontal surface by a horizontal force $F=\frac{2mg}{3}.$ Mass per unit length of the rod is given $\lambda \left(r\right)=\left(\frac{m}{l^2}r\right),$ where $r$ is distance from the action point of applied force $F$ and $l$ is the length of the rod. Then,