An insect crawls up a hemispherical surface very slowly, see Fig. 8.68. The coefficient of friction between the insect and the surface is $1/3$. If the line joining the centre of the hemispherical surface to the insect makes an angle a with the vertical, the maximum possible value of $\alpha$ is given by

Block $\mathrm{A}$  of mass is placed over the block  $\mathrm{B}$ of mass $8 kg$. The combination is placed over a rough horizontal surface, The coefficients of friction between $\mathrm{B}$ and the floor is $0.5$.The coefficient of friction between $\mathrm{A} \mathrm{and} \mathrm{B}$ is $0.4$ A horizontal force of $10N$ is applied on block B. The force of friction between$\mathrm{A} \mathrm{and} \mathrm{B}$ is:

Block $\mathrm{A}$ of mass $\mathrm{m}$ and block $\mathrm{B}$ of mass $2\mathrm{m}$ are placed on a fixed triangular wedge by means of a massless, inextensible string and a frictionless pulley as shown in. The wedge is inclined at $45°$ to the horizontal on both the sides. The coefficient of friction between the block $\mathrm{A}$ and the wedge is $\frac{2}{3}$ and that between the block $B$ and the wedge is $\frac{1}{3}$ and both the blocks $\mathrm{A}$ and $\mathrm{B}$ are released from rest, the acceleration of $\mathrm{A}$ will be:

Two masses $\mathrm{A}$ and $\mathrm{B}$ of $15 \mathrm{kg}$ and $10 \mathrm{kg}$ are connected with a string passing over a frictionless pulley fixed at the corner of a table, (as shown in Fig.) The coefficient of friction between the table and block is $0.4$. The minimum mass of $\mathrm{C}$, that may be placed on $A$ to prevent it from moving is

What is the maximum value of the force $\mathrm{F}$ such that the block shown in the arrangement,does not move?

A horizontal force of $10\mathrm{N}$ is necessary to just hold a block stationary against a wall. The coefficient of friction between the block and the wall is $0.2$. The weight of the block is: