Two wedges each of mass $600 \ g$ are placed next to each other on a rough horizontal surface. The coefficient of static friction between the wedges and the surface is $0.4$. $A$ cube of mass $M$ is balanced on the wedges as shown in the figure. If there is no friction between the cube and wedges,the largest mass $M$ of the cube that can be balanced without motion of the wedges is . . . . . . $kg$.

$A$ truck starting from rest moves with an acceleration of $5\,m/s^2$ for $1\,sec$ and then moves with constant velocity. The velocity w.r.t. ground v/s time graph for the block in the truck is (Assume that the block does not fall off the truck and the coefficient of friction $\mu = 0.2$):

$A$ ball is dropped on the floor from a height of $20 \ m$. It rebounds to a height of $5 \ m$. The ball remains in contact with the floor for $1 \ s$. The average acceleration during contact is (acceleration due to gravity $g = 10 \ m/s^2$): (in $m/s^2$)

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:

In the figure,a block of weight $60 \, N$ is placed on a rough surface. The coefficient of friction between the block and the surface is $0.5$. Find the maximum weight $W$ such that the block does not slip on the surface.

In the arrangement shown in the figure,if the blocks of masses $m$ and $2m$ are released from rest,find the tension in the string. (Given: $\mu_1 = 2/3$ for mass $m$,$\mu_2 = 1/3$ for mass $2m$,the string is massless and inextensible,and the pulley is frictionless.)