A spring loaded with a piece of metal extends by 10.5cm in air. When the metal is fully submerged in water, the spring extends by 6.8cm. Calculate the relative density of the metal. (Assume Hook's law is obeyed) extension in air \(e_1 = 10.5 cm\) extension in water \(e_2 = 6.8 cm\) change in extension \(e_3 = (e_1-e_2)\) Relative density of solid R.d = \(weight in air/apparent of loss weight in water\) We are not dealing with weights - we are dealing with lenght. Do we say weight is proportional to lenght? Thinking like that, we make us work like this \(R.d = e_1/e_3 = 10.5/3.7 = 2.84\) My question now is is weight propotion to lenght ?
Yes the weight is proportional to the length of the stretched spring. Hookes law: \(F = kX\) F = force in this case the weight k = spring constant X = displacement (length) So if X is doubled then F would be doubled.
