Find time (in $\mathrm{s}$), when block $B$ falls off the bracket. A $1 \mathrm{kg}$ block $B$ rests as shown on a frictionless bracket $A$ of same mass. Constant force $F=3 \mathrm{N}$ starts to act at time $t=0$, when the distance of block $B$ from the end of bracket is $13.5 \mathrm{m}$.

In figure shown, pulleys are ideal. Initially the system is in equilibrium and string connecting $m_2$ to rigid support below is cut. What is the initial acceleration (in $\mathrm{m} {\mathrm{s}}^{-2}$) of  $m_2$? (Given $m_1=9 \mathrm{kg}; m_2=3 \mathrm{kg})$

At $t=0$, the lower end of the bar $A$ is just above the upper end of bar $B$ (mass of bar, $A=3 \mathrm{kg}$, mass of bar, $B=\frac{11}{3} \mathrm{kg}$). Find the time when upper end of block $A$ just crosses the lower end of $B$. (Assume the system was released at $t=0$) $\left(g=10 \mathrm{m} {\mathrm{s}}^{-2}\right)$.

Two blocks $A$ and $B$ each of mass $m$ are placed on a smooth horizontal surface. Two horizontal forces $F$ and $2F$ are applied on both the blocks $A$ and $B$, respectively, as shown in figure. The block $A$ does not slide on block $B$. Find the normal reaction acting between the two blocks (in $\mathrm{N}$) if $F=10 \mathrm{N}$.

A small block of mass $m=2 \mathrm{kg}$ is kept at rest at the bottom of the inclined plane of a wedge of mass $M=9 \mathrm{kg}$. A force of $210 \mathrm{N}$ is applied on the wedge horizontally as shown in the diagram. All the surfaces are smooth. Determine the time taken in seconds by the mass $m$ to reach the highest point of the inclined plane of the wedge? $\left(g=10 \mathrm{m} {\mathrm{s}}^{-2}\right)$

In the system shown in figure, all surfaces are smooth and string and pulleys are light. Angle of wedge $\mathrm{\theta }={\sin }^{-1}\left(\frac{3}{5}\right)$. When released from rest, it was found that the wedge of mass $m_0$ does not move. Find $\frac{m}{M}$.

The upper surface of block $C$ is horizontal and its right part is inclined to the horizontal at angle $37°$. The mass of blocks $A$ and $B$ are $m_1=1.4 \mathrm{kg}$ and $m_2=5.5 \mathrm{kg}$, respectively. Neglect friction and mass of the pulley. Calculate acceleration $a$ with which block $C$ should be moved to the right so that $A$ and $B$ can remain stationary relative to it.