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? $[g = 10\, m/s^2]$

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

$A$ block is kept on a fixed smooth wedge whose vertical section is a curve $y = \frac{x^2}{\sqrt{3}}$ as shown in the figure,where $x$ represents the horizontal direction and $y$ represents the vertical direction. When released from a point where $y = \frac{1}{4\sqrt{3}}$,what will be its acceleration? $(g = 10 \ m/s^2)$

$A$ 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?

An object requires $500 \,N$ force to be pulled up on a $30^{\circ}$ frictionless smooth inclined plane at a constant speed. The weight of the object is

The horizontal acceleration that should be given to a smooth inclined plane of angle $\sin^{-1} (1/l)$ to keep an object stationary on the plane relative to the inclined plane is