Question

Solve this numerical problem. ​

Answer 1

$\huge\rm\underline\red{Question:-}$

A solid of density p has weight W. Show that it's apparent weight will be [1-(pL/p)] when it is completely immersed in a liquid of density pL.

$\huge\mathbb\green{Aηswer:-}$

→ Apparent weight of the solid = (Weight of solid in air) - (loss of weight of solid in liquid)

→ but, loss of weight of solid in liquid is equals to the weight of liquid displaced.

→ Thus, weight of liquid displaced is the product of Volume of solid and density of liquid.

$∴ Volume \: of \: solid = \: \frac{W}{D}$

where,

weight of solid = W

density = D

but, density of liquid = d.

→ Thus, weight of liquid displaced = w.d / D = Loss of weight of solid into liquid.

$∴ Apparent \: weight = \frac{W - W.d}{D}$

$= W(1 - \frac{ p_{1} }{p} )$ .

→ Hence, apparent weight of the solid is

$= W(1 - \frac{ p_{1} }{p} )$ .