It is easier to draw up a wooden block along an inclined plane than to haul it vertically,principally because

What should be the minimum force $P$ to be applied to the string so that a block of mass $M$ just begins to move up the frictionless inclined plane? The string passes over a pulley attached to the block,with one end fixed to the incline and the other pulled with force $P$ at an angle $\theta$ with the incline.

Two blocks of equal masses are tied to the ends of a light string. The string passes over a massless pulley fixed on a frictionless surface as shown in the figure. The acceleration of the centre of mass of the blocks is ($g$ = acceleration due to gravity).

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

As per the given figure,a weightless pulley $P$ is attached on a double inclined frictionless surface. The tension in the string (massless) will be (if $g = 10 \, m/s^2$):

$A$ body takes $4 \, s$ to reach the bottom of an inclined plane from the top. How much time (in $s$) will it take to cover one-fourth of the distance?