Question

13. A metal ball of density 7800 kg/m3

is suspected to have

a large numbr of inner cavities. It weighs 9.8 kg 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 approrximately

Answer 1

# Answer- volume of cavity/ball=0.16

# Explaination-

Here when put in water the water displaces/fills the empty cavity.

Volume of only metal=mass/density =9.8/7800=1.25×10^-3cu.m

Volume of whole ball including cavity= weight of water dispaced/density of water

Density of water is 1000kg/cu.m.

Volume of whole ball=1.5×10^-3cu.m

Volume of cavity=Volume of ball-volume of metal

=1.5×10^-3 - 1.25×10^-3

=0.25×10^-3cu.m

Ratio of volume of cavity/ball = 0.25×10^-3 / 1.5×10^-3 = 0.16 = 16%

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