A body weighs 10newton in air and 9.5 in water. How will it weigh in alchohol if density 0.8gcm-³

The weight of object in alcohol is, W₀ = 9.6 N

Explanation:

Given,

The weight of body in air, Wₐ = 10 N

The weight of the body in water, Wₓ = 9.5 N

The density of the alcohol, ρ = 0.8 g/cm³

= 800 kg/m³

The weight of body in water = weight of object in air - weight of water displaced

9.5 N = 10 N - weight of water displaced

Weight of water displaced = 0.5 N

The mass of the displaced water, m = 0.5 / 9.8

= 0.051 kg

Therefore the volume of the water displaced,

V = m / ρ

= 0.051 / 1000

= 5.1 x 10⁻⁵ m³

The volume of water displaced is equal to the volume of alcohol displaced

Therefore, the mass of the alcohol displaced, = V x ρ

= 5.1 x 10⁻⁵ x 800

= 0.0405 kg

The weight of the alcohol displaced, w = 0.0405 x 9.8

= 0.4 N

Therefore,

The weight of body in alcohol = weight of object in air - weight of alcohol displaced

W₀ = W - w

= 10 N - 0.4 N

= 9.6 N

Hence, the weight of object in alcohol is, W₀ = 9.6 N