Question

You are provided with a hollow iron ball A of volume 15 $c{m}^3$ and mass 12 g and a solid iron ball B of mass 12 g. Both are placed on the surface of water contained in a large tub.

(a) Find upthrust on each ball.
(b) Which ball wil sink ? Give reason for your answer. (Density of iron = 8.0 g $c{m}^{-3})$

Answer 1

a) Density of ball A $=\frac{12g}{15c{m}^3}=0.8g/c{m}^3$
Since its density is less than the density of water, which is $1g/c{m}^3$, it will float in water.
Hence, upthrust = Weight of the body = 12 gf

For solid sphere B, volume, $V=\frac{12g}{8g/c{m}^3}=1.5c{m}^3$
Hence, upthrust = Weight of water displaced $=1g/c{m}^3\times 1.5c{m}^3\times g=1.5gf$

(b) Density of ball A $=\frac{12g}{15c{m}^3}=0.8g/c{m}^3$
Since its density is less than the density of water, which is $1g/c{m}^3$, it will float in water.

The other ball, being a solid iron ball, has a density of $8g/c{m}^3$. As its density is greater than that of water, it will sink.