Question

A small block is freely sliding down from the top of a smooth inclined plane. The block reaches the bottom of the inclined plane then the block describes vertical circle of radius $0.5m$ along a smooth track. The minimum vertical height of the inclined plane should be:

• A. $1m$
• B. $1.25m$
• C. $3m$
• D. $2.5m$

Answer 1

Answer: (B)

$1.25m$

For completing a vertical circle, $v_{bottom}=\sqrt{5gR}$$=5m/s$
Applying conservation of energy from A to B:
$mgh=\frac{1}{2}m{v}^2$
or, $10h=\frac{(5{)}^2}{2}$
or, $h=1.25m$