$A$ truck of mass $30,000 \ kg$ moves up an inclined plane of slope $1$ in $100$ at a speed of $30 \ km/h$. The power of the truck is ................. $kW$ (given $g = 10 \ m/s^2$).

Two masses $M_1$ and $M_2$ are attached to the ends of a string which passes over a pulley attached to the top of a double inclined plane of angles of inclination $\alpha$ and $\beta$. If the system is released,the acceleration $a$ of the system is given by:

$A$ football of radius $R$ is kept on a hole of radius $r$ (where the diameter of the hole is $2r$ and $r < R$) made on a plank kept horizontally. One end of the plank is now lifted so that it gets tilted,making an angle $\theta$ with the horizontal as shown in the figure. The maximum value of $\theta$ such that the football does not start rolling down the plank satisfies (figure is schematic and not drawn to scale) -

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 $N$.

In the figure shown,$A$ and $B$ are free to move. All the surfaces are smooth. Then for $(0 < \theta < 90^o)$:

Find the acceleration of the system shown in the figure.