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Question

1000 m3 of sand is being poured on the ground. It accumulates on the ground in the shape of a conical pyramid. If the radius of the base of pyramid is 5 m, where is the centre of mass of the pile of sand located?

A
90π m from the centre of the base.
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B
30π m from the centre of the base.
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C
12π m from the top of the pyramid.
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D
3π m from the top of the pyramid.
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Solution

The correct option is B 30π m from the centre of the base.
Sand will pile up in the form of a solid cone
Given, radius of cone's base =R=5 m
Volume of solid cone V=13πR2H1000 m3=13×π×52×HH=300025π=120π m


The solid cone is symmetrical about an axis passing through its vertex and centre of the base, i.e y axis in the shown figure, so its COM will lie along y axis.
COM of solid cone (measured from centre of base) is given by y=H4
i.e yCM=H4=30π m

COM of the pile of sand will lie at a distance of 30π m from the centre of base

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