Question

A cone full of water, is placed on its side on a horizontal table, the thrust on its base is x time the weight of the contained fluid, where 2α is the vertical angle of the cone. Find the value of x.

(A) 3 cos α (B) 3 sin α (C) 2 sin α (D) 2 cos α

Answer 1

Correct option (B) 3 sin α

Explanation:

V is the vertex of the cone and VB is the generator in contact with the horizontal table.

A is the highest point of the cone and the horizontal plane passing through A is the level of the freesurface . Let α be the semi-vertical angle of the cone, then ∠AOL = α. Let h be the height of the cone, then the radius of the base of the cone = h tan α . Also the depth of O, the C. G. of the base of the cone below the free surface.

OL = AO cos α = h tanα cosα = h sin α

Thrust on the base of the cone

3 sin α [weight of the liquid contained in the cone]