in air an object weighs 15N when immersed in water it weighs 12N when immersed in another liquid weighs 13N. Determine the density of the object and that of the other liquid

Its volume displaced 3 Newtons of water

3 Newtons = mass of water * g
g is about 9.81m/s^2
so mass of water =3/9.81 =0.306 kg
Water density is about 1000 kg/meter^3
0.306 kg * 10^-3m^3/kg = 3.06 *10^-4 m^3 volume
so
15 kg/3.06*10^-4 m^3 = 4.9*10^4 kg/m^3

if you want grams/cm^3
4.9*10^4 * 10^-6 m^3/cm^3 * 10^3 g/kg =49 g/cm^3

the object displaces a fixed amount of liquid

the weight of "other liquid" displaced is 2/3 of the weight of water displaced

the density of the "other liquid" is 2/3 the density of water

a. M1*g = 15 N.

M1 = 15/g = 15/9.8 = 1.53 kg = mass of object in air.
M2 = 12/9.8 = 1.22 kg = mass of object when immersed.

M1-M2 = 1,53-1.22 = 0.31 kg lost = mass of water displaced.

V*Dw = 310 g.
V*1 = 310
V = 310 cm^3 of water displaced = Vol. of object.

Vo * Do = 1530 g.
310*Do = 1530
Do = 4.94 g/cm^3. = density of object.

b. M2*g = 13 N.
M2 = 13/g = 13/9.8 = 1.33 kg = mass of object when immersed.
M1-M2 = 1.53-1.33 = 0.20 kg lost = mass of liquid displaced.

Vol. of liquid = Vo = 310 cm^3.
V*D = 200 g.
310D = 200
D = 0.645 g/cm^3. = density of liquid.

how did the1530g come about ,because am a little bit confused.

1.53 kg = 1530 g.

To determine the density of an object and another liquid, we can use the concept of buoyancy. The difference in weight between an object in air and in a liquid is equal to the buoyant force acting on the object.

Let's start by finding the density of the object. The weight of the object in air is 15N, and when immersed in water, it weighs 12N. The difference in weight is 15N - 12N = 3N. This 3N difference in weight represents the buoyant force acting on the object in water.

The buoyant force is given by the equation:

Buoyant force = Weight of the fluid displaced by the object

Since the object is completely submerged in water, the buoyant force is equal to the weight of the water displaced by the object. Therefore, the weight of the water displaced by the object is also 3N.

Now, we can calculate the density of the object using the formula:

Density = Mass / Volume

The weight of the water displaced by the object is equal to the weight of the object immersed in water. So, we can substitute the weight of the object immersed in water (12N) into the density formula and solve for the density of the object.

Density of the object = Weight of the object immersed in water / Volume of the object

density of the object = 12N / (Volume of the object)

Unfortunately, to determine the density of the object, we need additional information such as the volume of the object. Without this information, we cannot determine the density of the object.

As for the density of the other liquid, we would need more information, such as the weight of the object when immersed in that liquid, or the volume and mass of the liquid. Without this information, we cannot determine the density of the other liquid either.

Therefore, without additional data, we cannot determine the density of the object or that of the other liquid.