An object weighs 258 N when fully immersed in water and 349 N when fully immersed in oil of specific gravity 0.79. What is the volume of the object (in liters)? The density of water is 998 kg/m3.

The weight of an object in a fluid is less than its weight in air due to the buoyant force. The buoyant force is equal to the weight of the fluid displaced by the object.

The weight of the object in water is 258 N, and the weight of the object in oil is 349 N. The difference in these weights is due to the difference in the buoyant forces in the two fluids.

The buoyant force in water is equal to the weight of the water displaced by the object, which is the volume of the object times the density of water times the acceleration due to gravity.

Similarly, the buoyant force in oil is equal to the volume of the object times the density of oil times the acceleration due to gravity.

The density of oil can be found by multiplying the specific gravity of the oil by the density of water.

So, the density of oil = 0.79 * 998 kg/m^3 = 788.22 kg/m^3

The difference in the weights of the object in the two fluids is equal to the difference in the buoyant forces, so we can write:

349 N - 258 N = (Volume * 788.22 kg/m^3 * 9.8 m/s^2) - (Volume * 998 kg/m^3 * 9.8 m/s^2)

Solving this equation for Volume gives:

Volume = (349 N - 258 N) / ((788.22 kg/m^3 - 998 kg/m^3) * 9.8 m/s^2)

Volume = 0.091 m^3

Since 1 m^3 = 1000 liters, the volume of the object is 0.091 m^3 * 1000 = 91 liters.