Question

A particle starts sliding down from the top of the smooth convex hemisphere of radius $30$$cm$, placed horizontally with convex side up. The vertical distance at which particle leaves the surface from it's highest point is:

• A. $5$$cm$
• B. $10$$cm$
• C. $15$$cm$
• D. $20$$cm$

Answer 1

Answer: (B)

$10$$cm$

$H=R(1-cos\theta )$
Using Work, Energy Theorem between A and B
$mgR(1-cos\theta )=\frac{1}{2}m{V}^2$
$V=\sqrt{2gR(1-cos\theta )}$

at B, normal becoms zero
$mgcos\theta =m\frac{V^2}{R}$
$gcos\theta =2g-2gcos\theta$
$cos\theta =\frac{2}{3}$
$H=R(1-cos\theta )$
$=\frac{R}{3}$
$=10cm$