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

$A$ block of mass $m$ is released from rest at point $A$ on an inclined plane of angle $\theta$ with the vertical. The block slides down and compresses a spring of spring constant $k$. Find the compression in the spring when the speed of the block is maximum.

$A$ 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 $(g)$.

For the given system,the acceleration of the system is ........... $ms^{-2}$ $(\sin 37^\circ = 0.60, \sin 53^\circ = 0.80)$.

Block $A$ of weight $100 \, N$ rests on a frictionless inclined plane of slope angle $30^{\circ}$. $A$ flexible cord attached to $A$ passes over a frictionless pulley and is connected to block $B$ of weight $w$. Find the weight $w$ for which the system is in equilibrium.

$A$ frictionless wire $AB$ is fixed on a circle of radius $R$. $A$ very small bead slips on this wire. The time taken by the bead to slip from $A$ to $B$ is: