Solid hemisphere resting on an inclined plane

[Jamessamuel]

Homework Statement

A solid uniform hemisphere rests in equilibrium with its curved surface in contact with a rough inclined plane which is elavated by an angle α where sin(α) = 3/16. Find the angle between the symmetry axis of the hemisphere and the vertical.[/B]

Homework Equations

Sine rule

The Attempt at a Solution

I drew the hemisphere as though slightly tilted - so that the line of action of the weight passed through the contact point of the hemisphere with the plane. However the answer shows the hemisphere so that the flat surface is vertical and not only do I fail to understand how this arrangement would keep it on equilibrium but also how I was supposed to know to draw it in this orientation.

 

[Jamessamuel]

 

[TSny]

You are right. The flat surface would not be vertical. Use the triangle shown on the right as a guide to drawing the hemisphere and incline.