$A$ block of mass $m_1 = 2\,kg$ on a smooth inclined plane at an angle of $30^\circ$ is connected to a second block of mass $m_2 = 3\,kg$ by a cord passing over a frictionless pulley as shown in the figure. The acceleration of each block is ....... $m/s^2$ (assume $g = 10\,m/s^2$).

$A$ 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 $........\,s$.

$A$ body sliding on a smooth inclined plane requires $4$ seconds to reach the bottom starting from rest at the top. How much time does it take to cover one-fourth distance starting from rest at the top?

$A$ car is moving on a plane inclined at $30^{\circ}$ to the horizontal with an acceleration of $10 \, ms^{-2}$ parallel to the plane upward. $A$ bob is suspended by a string from the roof of the car. The angle in degrees which the string makes with the vertical is ...... . (Take $g = 10 \, ms^{-2}$)

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

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