$A$ rod is constrained to move along a vertical wall and a horizontal floor. If the velocity of end $A$ is $V_A$ along the horizontal floor,find the velocity $V_B$ of end $B$ along the vertical wall in terms of $V_A$ and $\theta$.

If $m_1 = 4m_2$,what is the acceleration of $m_2$? The acceleration of $m_1$ is $a$.

$A$ frictionless cart $A$ of mass $100 \ kg$ carries two other frictionless carts $B$ and $C$ having masses $8 \ kg$ and $4 \ kg$ respectively,connected by a string passing over a pulley as shown in the figure. What horizontal force $F$ must be applied on the cart $A$ so that the smaller carts do not move relative to it (in $N$)? (Take $g = 10 \ m/s^2$)

In the pulley system shown in the figure, the mass of $A$ is half of that of $\text{rod } B$. The rod length is $500 \text{ cm}$. The mass of pulleys and the threads may be neglected. The mass $A$ is set at the same level as the lower end of the rod and then released. After releasing the mass $A$, it would reach the top end of the rod $B$ in time (Assume $g=10 \text{ m/s}^2$): (in $\text{ s}$)

Consider the situation shown in the figure. All the surfaces are smooth. The tension in the string connected to $2m$ is

In the given figure,the acceleration of wedge $A$ is $10 \ m/s^2$ along the inclined plane. There is no friction between $A$ and $B$,and between $A$ and the fixed inclined plane. Then the acceleration of block $B$ will be ............ $m/s^2$.