Question

A circular base cone is floating in liquid whose vertex is below surface of liquid. Then show that surface and surface of buoyancy is hyperparaboid.

Answer 1

Step-by-step explanation:

Buoyancy force = - Weight of fluid displaced by body

= Resultant of forces acting on the body due to pressure differences

Weight of fluid displaced acting downwards = (

3

1

π R

2

H)×ρg

Force acting on the bottom of cone acting upwards =(ρgH)×π R

2

(Assuming tip of cone is just touching the surface)

Net force acting sidewards on the cone is zero by symmetry.

Weight of fluid displaced by body(downwards) = Force acting on the bottom(upwards) - Force acting on the slant surface of cone

The force acting on the slant surface of the cone = (ρgHπ R

2

) - (

3

1

π R

2

Hρg)

=

3

2

πρgHR

2