Three weights $A, B$ and $C$ are connected by strings as shown in the figure. The system moves over a frictionless pulley. The tension in the string connecting $A$ and $B$ is (where $g$ is acceleration due to gravity):

$A$ constant force $F$ is applied in the horizontal direction as shown. If the contact force between $M$ and $m$ is $N$ and the contact force between $m$ and $M'$ is $N'$,then:

When the bomb $Q$ explodes,the trolley of mass $200 \, kg$ travels a distance of $36 \, m$ before coming to rest. What distance will the trolley of mass $300 \, kg$ travel before coming to rest (in $, m$)?

The figure shows an arrangement of a rod of length $l$ and mass $M$ and a bead of mass $m$ attached to a weightless string passing over a frictionless pulley. At $t = 0$,the bead is level with the lower end of the rod. The bead slides down the string with considerable friction and is opposite to the other end of the rod after $T$ seconds. Assuming friction between the bead and the string to be constant throughout,the frictional force is:

Imagine the situation in which the given arrangement is placed inside a trolley that can move only in the horizontal direction,as shown in the figure. If the trolley is accelerated horizontally along the positive $x$-axis with $a_0$,then identify the correct statement$(s)$ related to the tension $T$ in the string.

$A$ plank with a box on it at one end is gradually raised about the other end. As the angle of inclination with the horizontal reaches $30^o$,the box starts to slip and slides $4.0\, m$ down the plank in $4.0\, s$. The coefficients of static and kinetic friction between the box and the plank will be,respectively: