Three forces are acting on a particle of mass $m$ initially in equilibrium. If the first two forces ($R_1$ and $R_2$) are perpendicular to each other and suddenly the third force $\left(R_3\right)$ is removed, then the acceleration of the particle is

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 $2 \mathrm{s}$.

Block $B$ has mass $m$ and is released from rest when it is on top of wedge $A$ which has a mass$3m$. Determine the tension in cord $CD$ needed to hold the wedge from moving while $B$ is sliding down $A$. Neglect function.