A uniform, rigid, mass less (light) rod $AB$ of length ''$l$'" has two equal, masses "$m$" each as show. The rod is smoothly hinged at $A$.$C$ is the midpoint of the rod. The rod rotates in the vertical plane under critical condition.

A boy throws a cricket ball from the boundary to the wicket keeper. If the frictional force due to air $\left(f_a\right)$ cannot be ignored, the forces acting on the ball at the position $X$ are represented by

A maximum of $3 \mathrm{N}$ force can be applied on a block, down the incline, that would still not move the block which is placed on a rough inclined plane as shown in the figure. The maximum external force up the inclined plane that does not move the block is $12 \mathrm{N}$. The coefficient of static friction between the block and the plane is $\left[\mathrm{Take} g=10 \mathrm{m} {\mathrm{s}}^{-2}\right]$

Two masses connected in series with two massless strings are hanging from a support as shown in the figure. Find the tension in the upper string

Two blocks $A$ and $B$ are placed one over the other on a smooth horizontal surface. The maximum horizontal force that can be applied on lower block $A$, so that $A$ and $B$ move without separation is $49 \mathrm{N}$. The coefficient of friction between $A$ and $B$ is

The length of a metal wire is ${\ell }_1,$ when the tension in it is $T_1$ and is ${\ell }_2$ when the tension is $T_2.$ The natural length of the wire is: