Blocks shown in figure moves with constant velocity $10 \mathrm{m}\hspace{0.17em}{\mathrm{s}}^{-1}$ Towards right. All surfaces in contact are rough. The friction force applied by $B$ on $A$ is

A block of weight $W$ is supported by three strings as shown in figure. Which of the following relations is true for tension in the strings? (Here $T_1,T_2$ and $T_3$ are the tension in the strings $A, B$ and $C$ respectively)

A vehicle is moving on a road with an acceleration a $=20 \mathrm{m} {\mathrm{s}}^{-2}$ as shown in figure. The frictional coefficient between the block of mass $\left(m\right)$ and the vehicle so that block is does not fall downward is $\left(g=10 \mathrm{m} {\mathrm{s}}^{-2}\right)$

In the given arrangement all surfaces are smooth. What acceleration should be given to the system, for which the block $m_2$ doesn't slide down?

A trolley is falling freely on inclined plane as shown in the figure. The angle of string of pendulum with the ceiling of trolley is $\left(\alpha \right)$ equal to