Question

Determine the density of a solid sphere of radius 2 cm half floating in water?


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Answer 1

Answer:

Up thrust acting upon the sphere = vdg

Where 'd'’ is the density of water , 'g' is the acceleration due to gravity and 'v' is the immersed volume of the sphere

The sphere floats when its weight is equal to the upthrust act upon it by water .

Weight of the sphere = mg

But , mass(m) = volume(V) * density (D)

Where 'm' is the mass of the sphere and 'D’ is the density of the sphere and 'V' is the volume of the sphere .

As the sphere is half submerged , v = V/2

Therefore , vdg = mg

V/2 * d * g = V * D * g

So D = d/2

Density of the sphere is half the density of water . That is 1000kgm -³ / 2

D = 500kgm-³