A $30 \mathrm{kg}$ mass moving at $18.0 {\mathrm{ms}}^{-1}$ collides with a $90 \mathrm{kg}$ mass moving at  $14.4 {\mathrm{ms}}^{-1}$ in the opposite direction. The collision is elastic and head-on. Find the velocity of each mass after the collision.

A small block of mass $M$ moves on a frictionless surface of an inclined plane, as shown in the figure. The angle of the incline suddenly changes from ${60}^{\circ }$ to ${30}^{\circ }$at point B. The block is initially at rest at A. Assume that collisions between the block and incline are totally inelastic. $\left(g=10 \mathrm{m}/{\mathrm{s}}^2\right)$. The speed of the block at point $B$ immediately after it strikes the second incline is:

A small block of mass $M$ moves on a frictionless surface of an inclined plane, as shown in the figure. The angle of the incline suddenly changes from ${60}^{\circ }$ to ${30}^{\circ }$at point B. The block is initially at rest at A. Assume that collisions between the block and incline are totally inelastic. $\left(g=10 \mathrm{m}/{\mathrm{s}}^2\right)$. The speed of the block at point C, immediately before it leaves the second incline is:

A small block of mass $M$ moves on a frictionless surface of an inclined plane, as shown in the figure. The angle of the incline suddenly changes from ${60}^{\circ }$ to ${30}^{\circ }$at point B. The block is initially at rest at A. Assume that collisions between the block and incline are totally inelastic. $\left(g=10 \mathrm{m}/{\mathrm{s}}^2\right)$. 

A particle moves along $X$-axis from $x=0 to x=5 \mathrm{m}$ under a variable force $F=7-2x+3x^2 \mathrm{newton}$. The work done in the process is:

The work done on a particle of mass $m$ by a force $K\left[\frac{x}{{\left(x^2+y^2\right)}^{{\displaystyle \frac{3}{2}}}}\mathrm{i}+\frac{y}{{\left(x^2+y^2\right)}^{{\displaystyle \frac{3}{2}}}}\mathrm{j}\right]$ ($K$ being a constant of appropriate dimensions), when the particle is taken from the point $\left(a, 0\right)$ to the point $\left(0, a\right)$ along a circular path of radius $a$ about the origin in the $X-Y$ plane is: