A cylinder rests in a supporting carriage as shown. The side $AB$ of carriage makes an angle $30°$ with the horizontal and side $BC$ is vertical. The carriage lies on a fixed horizontal surface and is being pulled towards left with an horizontal acceleration $a$. The magnitude of normal reactions exerted by sides $AB$ and $BC$ of carriage on the cylinder be $N_{AB}$ and $N_{BC}$, respectively. Neglect friction everywhere. Then as the magnitude of acceleration $a$ of the carriage is increased, pick up the correct statement.

 

Surface between $30 \mathrm{kg}$ block and ground is smooth and between the blocks ${\mu }_s=0.4$ and ${\mu }_k=0.2.$ If $100 \mathrm{N}$ force is applied on $20 \mathrm{kg}$ block as shown then what will be the frictional force acting on it (in Newton)

Value of $\mathrm{\theta }$ is increased gradually from $\mathrm{\theta }=0.$ At $\mathrm{\theta }={\tan }^{-1}\left(\frac{1}{2}\right)$ both the blocks just start slipping. Than value of ${\mu }_2$ is: $\left(g=10 \mathrm{m} {\mathrm{s}}^{-2}\right)$

In the given diagram what is the minimum force $\text{'}F\text{'}$ required, so that block $\text{'}A\text{'}$ will slip on block $\text{'}B\text{'}$?

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