Question

The loss in weight of a solid when immersed in a liquid at 0°C is `W_1` and at t°C it is W. If the cubical expansion coefficient of solid and liquid are `gamma_s` and `gamma_l` resp then W is equal to?

Answer 1

Archimedes principle states that Loss of weight of an object when immersed in a fluid is equal to upthrust, which is equal to weight of the fluid displaced and acts in the upward direction at the center of mass of the displaced fluid.

Let `V_0` be initial volume of the solid. Therefore at `0^@"C"` we have

`W_1=V_0rhog` ......(1)
where `rho` is the density of the liquid and `g` is acceleration due to gravity.

At temperature `t^@"C"`, volume of solid becomes

`V=V_0(1+gamma_s(t-0))`
`=>V=V_0(1+gamma_st)`

Density is inversely proportional to volume . Therefore density of liquid at temperature `t^@"C"` is found by the expression

`rho_t=rho/(1+gamma_l t)`

Therefore we get

`W=V_0(1+gamma_st)rho/(1+gamma_l t)g`

Using (1) we get `W` in terms of `W_1`

`W=W_1(1+gamma_st)/(1+gamma_l t)`