Question

7.
A cube of edge length 20 cm is just balanced in two
immiscible liquids A and B as shown in figure. If A
and B has specific gravity 0.7 and 0.3 respectively,
then mass of the cube will be

(1) 2.34 kg
(3) 1.02 kg
(2) 3.36 kg
(4) 2.56 kg​

Answer 1

Answer:

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Answer 2

The mass of the cube is 4 kg.

Explanation:

Given:

    A cube of length 's' = 20cm.

    Liquid A has specific gravity = .7

    Liquid B has specific gravity = .3

Solution:

         We know that the density of water 'ρ' = 1 $g/cm^{2}$

         We also know the formula of specific gravity.

Specific gravity is the ratio of density of the object to the density of water.

 

                       Specific gravity = $\frac{density \\ of the\\ object}{density of water at \\ \\ 4^{o} c}$

So, volume of the cube = $s^{3}$,             where 's' id the side of the cube

     volume 'V' = 20 x 20 x 20

                        = $8\times10^{3} cm^{3}$

Body is equally immersed in voth the liquid. Voluem taken is just half.

                    Specific gravity s.p = $\frac{\frac{mass}{4\times10^{3} } }{1}$

For, lquid A,

Mass 'm' = $4\times10^{3} cm^{3}\times 0.7$

               = 2.8 x $10^{3} cm^{3}$

For, liquid B,  

Mass 'm' = $4\times10^{3} cm^{3}\times 0.3$

              = 1.2 x $10^{3} cm^{3}$

             

Add both tha masses and hence, mass of the cube is 4 x $10^{3} g$ which is 4 kg.