For the system shown in the figure,if $M_1 = 10 \ kg$,$M_2 = 5 \ kg$,$\theta = 30^\circ$,and $g = 10 \ m/s^2$,find the tension in the string in $N$.

$A$ body starts falling freely from height $H$ and hits an inclined plane in its path at height $h$ from the ground. As a result of this perfectly elastic impact,the direction of the velocity of the body becomes horizontal. The value of $\frac{H}{h}$ for which the body will take the maximum time to reach the ground is . . . . . . .

$A$ double inclined plane as shown in the figure has a fixed horizontal base and smooth faces with the same angle of inclination of $30^{\circ}$. $A$ block of mass $m_2 = 300 \ g$ is on one face and is connected by a cord passing over a frictionless pulley to a second block of mass $m_1 = 200 \ g$ kept on the other face. The acceleration with which the system of the blocks moves is ........ $\%$ of acceleration due to gravity $(g)$.

$A$ block of mass $m_1 = 2\,kg$ on a smooth inclined plane at an angle of $30^\circ$ is connected to a second block of mass $m_2 = 3\,kg$ by a cord passing over a frictionless pulley as shown in the figure. The acceleration of each block is ....... $m/s^2$ (assume $g = 10\,m/s^2$).

$A$ perfectly smooth sphere $A$ of mass $2 \ kg$ is in contact with a rectangular block $B$ of mass $4 \ kg$ and a vertical wall as shown in the figure. All surfaces are smooth. Find the normal reaction exerted by the vertical wall on sphere $A$ (in $N$). Take $g = 10 \ m/s^2$.

Consider the shown arrangement. Assume all surfaces to be smooth. If $N$ represents the magnitude of the normal reaction between the block of mass $m$ and the wedge of mass $M$,then the acceleration of $M$ along the horizontal equals: