Question

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

Answer 1

D) 3.0

Step-by-step explanation:

As we know that

`The\ specific\ gravity\ of\ fluid = (density\ of\ fluid)/(density\ of\ water \ at\ 4\ C) = (\rho_f)/(1,000)`

`0.6 = (\rho_f)/(1000)`

So,

`\rho_f = 600`

Now

T = True weight of object

= mg

`= 25 * 9.8`

= 245 N

W = apparent weight = 200 N

`\sigma` = density of object

Now we use the formula

buoyancy force = True weight - W

`\rho_f V g = 245 - 200`

600 V (9.8) = 45

V = 0.007653

m = 25 kg

And as we know that

`\sigma = (m)/(V)`

`= (25)/(0.007653)`

= 3266.7

Now

specific gravity is

`= (\sigma)/(water\ density)`

`= (3266.7)/(1000)`

= 3.2

Hence, the correct option is d.