Cone On An Inclined Plane?

Classical Mechanics Level 4

A uniform solid cone is placed on an inclined plane as shown above at the limiting case. Find $\tan \alpha$ if $\theta = 45^\circ$ .

1 solution

Md Zuhair
Aug 28, 2016

Here we have to use torque here. If we draw the FBD it will look like

Now our equation as $\text {Net Clockwise Torque = Net Anticlockwise Torque}$

Hence Our equations stands to be ,

mgcos $\theta$ x htan $\alpha$ = mgsin $\theta$ x h/4 [ $\large \text{ As h/4 is the COM of a cone.}$ ]

Solving We Get ,

tan $\alpha$ = 1/4 tan $\theta$

hence tan $\alpha$ = $0.25$ is the ans