Question

A solid of density 2.7gcm-3 and of volume 0.0015 m3
is completely immersed in alcohol of density 800 kgm-3
. Calculate in
SI unit:
(i) Weight of the solid.
(ii) Upthrust on solid.
(iii) Apparent weight of the solid in alcohol.

Answer 1

AnswEr

GiveN that,

• Density of the solid, ρ = 2700 kgm³

• Density of alcohol, ρ' = 800 kgm³

• Volume of water, V = 0.0015 m³

In order to calculate the required values we've general formula's instead of any other lengthy methods. Here, we can directly use the formulas by substituting their respective values.

I) Weight of the Solid.

This is given by,

⇒ Mass = Volume × Density

⇒ Mass = 0.0015 × 2700

⇒ Mass = 4.05 kg.

Now,

⇒ Weight of the solid = Mass × Acceleration due to gravity

⇒ Weight of the solid = 4.05 × 9.8

⇒ Weight of the solid = 40.5 N

II) Upthrust on solid.

To calculate the upthrust we've the Volume of alcohol & Solid.

Mass of alcohol :

⇒ m = V × ρ

⇒ m = 0.0015 × 800

⇒ m = 1.2 kg (approx.)

So,

⇒ Upthrust = Mass of alcohol × Acceleration due to gravity

⇒ Upthrust = 1.2 × 9.8

⇒ Upthrust = 12 N (approx.)

III) Apparent weight of the solid in alcohol.

Here, we'll directly use the formula,

⇒ Apparent weight = Weight of Solid - Upthrust

⇒ Apparent weight = 40.5 - 12

⇒ Apparent weight = 28.5 N