Question

A metal ball of density $7800kg/m^3$ is suspected to have a large number of inner cavities. It weighs $9.8kg$ when weighed directly on a balance and $1.5kg$ less when immersed in water. The fraction by volume of the cavities in the metal ball is approximately:

• A. $20\%$
• B. $30\%$
• C. $16\%$
• D. $11\%$

Answer 1

The correct option is C $16\%$

when metal ball put in water the water displaces/fills the empty cavity.

Volume of only metal=$mass/density=9.8/7800=1.25\times {10}^{-}3m^3$

Volume of whole ball including cavity=$V_b=\frac{W_d}{{\rho }_w}$

where $W_d$ is weight of water displaced

Density of water is ${\rho }_w=1000kg/m^3$.

Volume of whole ball=$1.5\times {10}^{-}3m^3$

Volume of cavity= $V_c=V_b-V_m$

where $V_b$ and $V_m$ are Volume of ball and volume of metal respectively

$V_c=1.5\times {10}^{-}3-1.25\times {10}^{-}3$

$V_c=0.25\times {10}^{-}3m^3$

Ratio of volume of cavity/ball = $\frac{0.25\times {10}^{-}3}{1.5\times {10}^{-}3}=0.16=16\%$

0.16 fraction of whole ball is a cavity. i.e. $16\%.$