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 $60^°$ to $30^°$ 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)

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.

$h = \sqrt{3}\,tan\,60^{\circ} = 3\,m$
Velocity immediately after it strikes the second line
$v = \sqrt{2\,gh}\,cos\,30^{\circ}$
$= \sqrt{2 \times10 \times3}\times \frac{\sqrt{3}}{2}$
$= \sqrt{45}\,m/s$.