A block of mass $m$ is kept on a plank. The coefficient of friction between the plank and block is $1.$The plank is slowly raised from one end so that it makes angle $\theta$ with horizontal. The forces of friction acting on the plank, when $\theta =30°$ and $\theta =60°$are respectively,

A force of $100 \mathrm{N}$ is applied on a block of mass $3 \mathrm{kg}$, as shown in the figure. The coefficient of friction between the surface and the block is $\frac{1}{4}$. The frictional force acting on the block, to keep it at rest, is

A block of mass $5 \mathrm{kg}$ is placed on a rough horizontal plane. The coefficients of static and kinetic friction between the block and surface are $0.5$ and $0.3$ respectively. A force of $100 \mathrm{N}$ is applied at an angle $30°$ with the horizontal as shown in the figure. The acceleration of the block will be $\left[g=10 \mathrm{m} {\mathrm{s}}^{-2}\right]$

In the given figure the co-efficient of friction between the block and the incline plane is $\text{'}1\text{'}.$ The acceleration with which the system should be accelerated so that the friction between the block and the wedge becomes zero $\left(g=10 \mathrm{m} {\mathrm{s}}^{-2}\right)$ is

A force of $49 \mathrm{N}$ is just able to move a block of wood weighing $10 \mathrm{kg}$on a rough horizontal surface, then coefficient of friction is

Find the compression in the spring if the system shown below is in equilibrium.

All surfaces shown in the figure are frictionless. A block of mass $2 \mathrm{kg}$ is kept on a wedge of mass $10 \mathrm{kg}.$ If the mass $m$ remains stationary w.r.t. wedge, the magnitude of force $P$ is $\left(g=10 \mathrm{m} {\mathrm{s}}^{-2}\right)$

A circular track of radius $600 \mathrm{m}$ is to be designed for vehicles passing at an average speed of $54 \mathrm{km} {\mathrm{hr}}^{–1}.$ The required angle of banking is