Question

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 ${60}^{\circ }$ and ${30}^{\circ }$ at point $B$.
The block is initially at rest at $A$. Assume that collisions between the block and the incline are totally inelastic. The speed of the block at point $B$ immediately after it strikes the second incline is

• A. $\sqrt{60}m/s$
• B. $\sqrt{45}m/s$
• C. $\sqrt{30}m/s$
• D. $\sqrt{15}m/s$

Answer 1

Answer: (B)

$\sqrt{45}m/s$

At point $B$ the block has an inelastic collision with the incline, so component of velocity perpendicular to incline plane becomes zero and component parallel to second surface is retained.
$h=\sqrt{3}\tan {60}^{\circ }=3m$
Velocity immediately after it strikes the second line
$v=\sqrt{2gh}\cos {30}^{\circ }=\sqrt{2\times 10\times 3}\times \frac{\sqrt{2}}{2}=\sqrt{45}m/s$.