A body of volume 100 cm³ weighs 5 kgf in air. It is completely immersed in a liquid of density 1.8 x 10³ kg m^-3. Find (i) the upthrust due to liquid and (ii) the weight of the body in liquid.

(i) As we know,

Upthrust due to liquid = volume of the solid x density of fluid x acceleration due to gravity

Given,

Volume of the body = 100 cm³

Converting cm³ into m³

100 cm = 1 m

So, 100 cm x 100 cm x 100 cm = 1 m³

Hence, 100 cm³ = $\dfrac{1 \times 100}{10,00,000}$

Therefore, V = 10^-4 m³

Weight of the body in air = 5 kgf

Density of the liquid = 1.8 x 10³ kg m^-3

Substituting the values in the formula above we get,

Upthrust = 10^-4 x 1.8 x 10³ x g = 0.18 kgf

Hence, the upthrust due to liquid = 0.18 kgf

(ii) weight of the body in liquid = weight of the body in air – upthrust

Substituting the values in the formula above, we get,

weight of the body in liquid = 5 kgf - 0.18 kgf = 4.82 kgf

Hence, weight of the body in liquid = 4.82 kgf