Question

Find the ratio of the weights, as measured by a spring balance, of a 1 kg block of iron and 1 kg block of wood. Density of iron =7800 kg/m³, density of wood =800 kg/m³ and density of air =1.293 kg/m³.

Answer 1

Answer:-  = 1.00153

Step by Step Solution:-

First We  calculate for  Iron:-

Mass of  iron =  1 kg

Density of  iron block = 7800kg/m³

Volume of  Iron block  = Mass/Density

                                     = 1/7800

                                     = 0.000128 m³

                                    = 1.28 × 10⁻⁴ m³

Upthrust due to air = V of iron block × Density of Air × g

                                = 1.28 × 10⁻⁴ × 1.293 × g

                                 = (1.655 ×  10⁻⁴)g N

Original Weight of iron block = m × g

                                    = 1 × g

                                    = g N

Weight of  iron block measured by spring balance,

W₁ = Original Weight of iron block - Upthrust due to air

W₁ = g(1 - 1.655 ×  10⁻⁴)

W₁ = 0.99983g N

Now , calculate for  Wood:-,

Mass of  wood =  1 kg

Density of  wood block = 800kg/m³

Volume of  wood block  = Mass/Density

                                     = 1/800

                                     = 0.00125 m³

                                     = 1.25 × 10⁻³ m³

Upthrust due to air = V of wood block × Density of Air × g

                                = 1.25 × 10⁻³  × 1.293 × g

                                 = (1.61625 ×  10⁻³)g N

Original Weight of wood block = m × g

                                    = 1 × g

                                   = g N

Weight of  wood block measured by spring balance,

W₂ = Original Weight of wood block - Upthrust due to air

W₂ = g(1 - 1.61625 ×  10⁻³)

W₂ = 0.9983g N

Now,

W₁/W₂ = 0.99983/0.9983

          = 1.00153

Answer 2

In Vacuum, Spring valance measures the accurate weight, but in air, the weight measured by the spring balance is changed because of the upthrust offered by the Air.

Reading of the Spring Balance = Weight of object.  [When in Vacuum].

In air, Upthrust acts upwards, therefore,

Reading of Spring Balance + Upthrust by air = Weight of object.

Reading of Spring Balance = Weight of object - Upthrust by air.

For, Iron,

  Weight = mass × g

  = 1 × 9.8

  = 9.8 N

Upthrust = Volume immersed × Density of air × g

 = mass of iron/density of iron × density of air × g

 = 1/7800 × 1.293 × g

 =  1.293/7800 × g N

∴ Reading of spring Balance or weight measured by it =  9.8 -  1.293/7800 × 9.8

= 9.8[1 - 1.293/7800.]

= 9.79 N.

For Wood,

Weight = Mass × g

= 1 × g

= 9.8 N.

Upthrust = mass of wood/density of wood × density of air × g

= 1/800 × 1.293 × 9.8

= 1.293/800 × 9.8

∴ Reading of spring balance or weight measured by spring balance = 9.8 - 1.293/800 × 9.8

= 9.8[1 - 1.293/800].

= 9.78 N .

Ratio of the weights = Weight measured for iron/Weight measured for Wood

= 9.79/9.78

= 1.001

Hope it helps.