Question

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

Answer 1

Let m be the mass of the object.
Actual weight of the object, W = 50 gf
Apparent weight of the object, $W_a=44gf$
Let the buoyancy be B.
Now, $W_a=W-B$
$\Rightarrow B=50g-44g$
\(\Rightarrow B = 6~dyne\)
This is the upthrust on the object.
Let ‘d’ be the density of the object, and ‘V’ be its volume.
Weight, W = Vdg = 50g
$\Rightarrow Vd=50$
The buoyancy is given by,
B = V(density of water )g
$\Rightarrow B=V\left(1000\right)g=6g$
$\Rightarrow V=\frac{6}{1000}=0.006m^3$
This is the volume of the object.
Now, $\Rightarrow d=\frac{50}{V}=\frac{50}{0.006}$
$\Rightarrow d=8333.33kg/m^3$
This is the density of the solid.