# A sample of an unknown material weighs 305.0 N in air and 219.0 N in alcohol solution with a density of 0.70 x 10^3 kg/m^3. What is the density of the material?

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### 1 Answer

The sample of the unknown material weighs 305 N in air. It has a mass of 305/9.8 = 31.12 kg. The sample when immersed in alcohol with a density of 0.7*10^3 kg/m^3 weighs 219 N. The mass of the sample as measured by a weighing scale is 22.34 kg.

When an object is immersed in a fluid it displaces a volume of the fluid equal to the volume of the object. Due to this there is upward force exerted on the body that reduces its weight. When a weighing scale is used to measure the mass of the body, the reduction in its weight reflects as a reduction in its mass.

The object loses an equivalent mass of 8.78 kg when it is immersed in alcohol. The density of alcohol is equal to 0.7*10^3 kg/m^3. Let the volume of the object be V. This gives V*0.7*10^3 = 8.78

=> V = 12.54*10^-3 m^3

This volume has a mass of 31.12 kg. The density of the material is 31.12/12.54*10^-3 = 2.48*10^3 kg/m^3