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

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

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

$A$ 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? $(g = 10 \ m/s^2)$

Consider the shown arrangement. Assume all surfaces to be smooth. If $N$ represents the magnitude of the normal reaction between the block of mass $m$ and the wedge of mass $M$,then the acceleration of $M$ along the horizontal equals:

Find the reading of the spring balance as shown in the figure. Assume that mass $M$ is in equilibrium and the block of mass $2.5 \text{ kg}$ is also in equilibrium. All surfaces are smooth. (Take $g = 10 \text{ m/s}^2$) (in $\text{ N}$)