$A$ truck of mass $10,000\, kg$ moves up an inclined plane rising $1$ in $50$ with a speed of $36\, km/h$. Find the power of the engine in $kW$ $(g = 10\, m/s^2)$.

$A$ 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) -

$A$ 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 $g = 10\,m/s^2$).

The time taken by a block of wood (initially at rest) to slide down a smooth inclined plane $9.8 \ m$ long (angle of inclination is $30^o$) is ......... $sec$.

What is the normal force on a body of mass $m$ placed on an inclined plane of angle $\theta$?

Two smooth inclined planes $A$ and $B$ each of height $20 \ m$ have angles of inclination $30^{\circ}$ and $60^{\circ}$ respectively. If $t_1$ and $t_2$ are respectively the times taken by two blocks to reach the bottom of the planes $A$ and $B$ from the top,then $t_1 - t_2 = $ (Acceleration due to gravity $= 10 \ m \ s^{-2}$)