Question

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, density of wood = 800 kg m−3 and density of air = 1.293 kg m−3.

Answer 1

The perceptible weight ratio = 1.0015

Explanation:

Step 1:

The balance in the spring tests the weight of an object. It will represent the same weight in the vacuum for the given iron and the wood block, but in the air, a buoyancy force will act on both blocks which will be equal to the weight of the displaced air.

Volume of a block of iron =$1/7800m^3$        

Wooden block volume  = $1/800m^3$

Step 2:

Air weight displaced by an iron block $=1.293\times1/7800 kg$

$=1.293/7800 kg$  

Air weight displaced by wooden block  $=1.293\times1/800 kg$  

$=1.293/800 kg$  

Step 3:

The iron block's apparent weight, shown in the spring balance $=1-1.293/7800 kg$  

$=(7800-1.293)/7800 kg$  

$=7798.707/7800 kg$

Apparent wooden block weight shown in the spring balance $=1-1.293/800 kg$    

$=(800-1.293)/800kg$

$=798.707/800$

Hence the perceptible weight ratio $=(7798.707/7800)/(798.707/800 )$      

$=(7798.707 \times 800)/(7800 \times798.707)$

$=1.0015$