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 ............ $m/s^2$.

In each of the three arrangements,the block of mass $m_1$ is being pulled left with constant velocity $v$. There is no friction anywhere. The strings are light and inextensible and pulleys are massless. The ratio of the speed of the block of mass $m_2$ in the three cases respectively is

In the arrangement shown in the figure,$a_{1}, a_{2}, a_{3}$ and $a_{4}$ are the accelerations of masses $m_{1}, m_{2}, m_{3}$ and $m_{4}$ respectively. Which of the following relations is true for this arrangement?

$A$ rod of length $L$ leans against a smooth vertical wall while its other end is on a smooth floor. The end that leans against the wall moves uniformly vertically downward. Select the correct alternative.

The pulleys in the diagram are all smooth and light. The acceleration of $A$ is $a$ upwards and the acceleration of $C$ is $f$ downwards. The acceleration of $B$ is

If the acceleration of block $A$ is $2\,m/s^2$ to the left and the acceleration of block $B$ is $1\,m/s^2$ to the left,then find the acceleration of block $C$.