Find the acceleration of $3 \mathrm{kg}$ mass when acceleration of $2 \mathrm{kg}$ mass is $2 \mathrm{m} {\mathrm{s}}^{-2}$ as shown in the figure.

  

Find the reading of spring balance as shown in the figure. Assume that mass $M$ is in equilibrium. (All surfaces are smooth)

Two blocks of masses $m_1$and $m_2$ are in equilibrium. The block $m_2$ hangs from a fixed smooth pulley by an inextensible string that is fitted with a light spring of stiffness $k$ as shown in the figure. Neglecting friction and mass of the string, find the acceleration of the bodies just after the string $S$ is cut. 

An inclined plane makes an angle $30°$ with the horizontal. A groove $\left(OA\right)$ of length $5 \mathrm{m}$ cut in the plane makes an angle $30°$
with $OX$. A short smooth cylinder is free to slide down under the influence of gravity. The time taken by the cylinder to reach from $A$ to $O$ is $(g=10 \mathrm{m} {\mathrm{s}}^{-2})$

The small marble is projected with a velocity of $10 \mathrm{m} {\mathrm{s}}^{-1}$ in a direction $45°$ from the horizontal $y$-direction on the smooth inclined plane. Calculate the magnitude $v$ of its velocity after $2 \mathrm{s}$.