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A 25 kg object has an apparent weight of 200 N when placed in a fluid with a specific gravity of 0.6. What is the specific gravity of the object? (By definition, the specific gravity of an object or fluid is the density of the object/fluid divided by the density of water...effectively making a dimensionless density). A) 1.2 B) 2.0 C) 12 D) 3.0

Respuesta :

Answer:

D) 3.0

Explanation:

As we know that

[tex]The\ specific\ gravity\ of\ fluid = \frac{density\ of\ fluid}{density\ of\ water \ at\ 4\ C} = \frac{\rho_f}{1,000}[/tex]

[tex]0.6 = \frac{\rho_f}{1000}[/tex]

So,

[tex]\rho_f = 600[/tex]

Now

T = True weight of object

= mg

[tex]= 25 \times 9.8[/tex]

= 245 N

W = apparent weight = 200 N

[tex]\sigma[/tex] = density of object

Now we use the formula

buoyancy force = True weight - W

[tex]\rho_f V g = 245 - 200[/tex]

600 V (9.8) = 45

V = 0.007653

m = 25 kg

And as we know that

[tex]\sigma = \frac{m}{V}[/tex]

[tex]= \frac{25}{0.007653}[/tex]

= 3266.7

Now  

specific gravity is

[tex]= \frac{\sigma}{water\ density}[/tex]

[tex]= \frac{3266.7}{1000}[/tex]

= 3.2  

Hence, the correct option is d.

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