In the arrangement shown,the $2\, kg$ block is held to keep the system at rest. The string and pulley are ideal. When the $2\, kg$ block is set free,by what amount does the tension in the string change? $[g = 10\, m/s^2]$

Two blocks each of mass $M$ are resting on a frictionless inclined plane as shown in the figure. Then:

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

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.

$A$ block '$A$' takes $2\,s$ to slide down a frictionless incline of $30^{\circ}$ and length '$l$',kept inside a lift going up with uniform velocity '$v$'. If the incline is changed to $45^{\circ}$,the time taken by the block to slide down the incline will be approximately $........\,s$.

$A$ 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.