Find the ratio of the weights, as measured by a spring balance, of a 1 kg block of iron and a 1 kg block of wood. Density of iron = 7800 kg/m^3,
Find the ratio of the weights, as measured by a spring balance, of a 1 kg block of iron and a 1 kg block of wood. Density of iron = 7800 kg/m3, density of wood = 800 kg/m3 and density of air = 1.293 kg/m a.
1 Answers
The spring balance measures the weight of an object. It will show the same weight for the given iron and the wood block in the vacuum but in the air, a force of buoyancy will act on both the blocks which will be equal to the weight of the air displaced.
The volume of iron block = 1/7800 m³
The volume of wooden block = 1/800 m³
The weight of air displaced by iron block =1.293*1/7800 kg
=1.293/7800 kg
The weight of air displaced by wooden block =1.293*1/800 kg
=1.293/800 kg
The apparent weight of the iron block shown in the spring balance =1-1.293/7800 kg
=(7800-1.293)/7800 kg
= 7798.707/7800 kg
The apparent weight of the wooden block shown in the spring balance =1-1.293/800 kg
=(800-1.293)/800 kg
= 798.707/800 kg
Hence the ratio of the apparent weights =(7798.707/7800)/(798.707/800)
=(7798.707*800)/(7800*798.707)
=1.0015