A spring balance reads 10 kg when a bucket of water is suspended from it. What is the reading on the spring balance when (i) an ice cube of mass 1.5 kg is put into the bucket (ii) an iron piece of mass 7.8 kg suspended by another spring is immersed with half its volume inside the water n the bucket. Relative density of iron = 7.8

Explanation

(i) Reading of a spring balance is equal to the reaction of force acting on it due to weight of object suspended from it.
So, when ice is put into the bucket, its total weight =10+1.5 =11.5 kg f
Reading of spring balance =11.5 kg f
(ii) Mass of iron peice, m=7.8 kg
R.D. of iron =7.8
Density of iron,
`p="R.D. "xx " Density of water"`
`=7.8 xx 10^(3) kg//m^(3)`
Volume of iron piece `=m/p=(7.8)/(7.8 xx 10^(3))=0.001 m^(3)`
Upthrust =Weight of water displaced
=Volume of water displaced `xx " Density of water "xx g`
`=(0.001)/(2) xx 10^3 xx g=0.5 kg f`
Total upward reaction =10+0.5 =10.5 kg f
Reading on the spring balance =10.5 kg f