Question

A solid weighs 30 gf in air and 26 gf when completely immersed in a liquid of relative density 0.8. Find: (i) the volume of the solid, and (ii) the relative density of the solid.

Answer 1

Answer:

The volume of the solid is 5 cm^3

The R.D. of the solid is 6

Explanation:

It is stated that,

The weight of the solid in air (w1) = 30 gf

The weight of the solid in a specific liquid (w2) = 26 gf

Relative density (R.D.) of the liquid = 0.8

So, it can be concluded that the density of the liquid is 8 g cm^-3

(i) Let, the volume of the solid be, 'v'

Weight of the liquid displaced

= volume of the liquid displaced* density of liquid * g

= v * 0.8* g* dyne

= 0.8v gf

When the solid is immersed in water then its weight gets lossed by_

(w1 -w2)

= (30-26)

= 4 gf

Though it should have to be noted here that the weight of the liquid gets displaced while the solid is immersed in the liquid is equal to the weight of the solid while immersed in the liquid.

From the above calculations we get that,

v*0.8 = 4

→ v = 4/0.8

→ v = 5 cm ^3

So, the volume of the solid is 5 cm^3

(ii) It is stated that,

The weight of the solid is 30 gf

So, it can be concluded that the mass of the solid = 30 g

∴ The density of the solid

$= \frac{mass}{volume} \\=\frac{30}{5} \\= 6 g cm^-3$

Hence, the relative density (R.D.) of the liquid

$\frac{6}{1} \\= 6$

So, the R.D. of the solid is 6

∵ The density of water is 1 g / cm^3.

∵ Relative density(R.D.)= Density of the substance/Density of water.

∵ There is no unit for relative density.

Answer 2

Answer:

Given, weight of solid in air = 30 gf and weight of solid in liquid = 26 gf., R.D of liquid = 0.8

Therefore, Density of liquid = 0.8 g cm-3

(i) Let V be the volume of the solid.

Weight of liquid displaced = Volume of liquid displaced xdensity of liquid x g

                                         = V 0.8g dyne

                                        = V 0.8 gf

Loss in the weight of the solid when immersed in the liquid = 30 - 26 = 4gf

But the weight of liquid displaced is equal to the loss in weight of the solid when immersed in liquid.

Therefore, Vx0.8 = 4 or V =  = 5 .

(ii) Given, weight of solid = 30gf

Therefore, Mass of solid = 30 g

Density of solid =  

Hence relative density of solid = 6