A solid weighs 50 gf in air and 44 gf in when completely immersed in water. Calculate
(i) the upthrust (ii) volume of the solid and (iii) the relative density of the solid

Let m be the mass of the object.

Actual weight of the object, W = 50 gf = 50g N

Apparent weight of the object, W_a = 44 gf = 44g N

Let the buoyancy be B.

Now,

W_a = W – B

=> B = 50g – 44g

=> B = 6g N

This is the upthrust on the object.

Let ‘d’ be the density of the object, and ‘V’ be its volume.

Weight, W = Vdg = 50g

=> Vd = 50

The buoyancy is given by,

B = V(density of water)g

=> B = V(1000)g = 6g

=> V = 6/1000 = 0.006 m³

This is the volume of the object.

Now, Vd = 50

=> d = 50/V = 50/0.006

=> d = 8333.33 kg/m³

This is the density of the solid.