Question

A box of mass 308 kg weighs 623 N when submerged in a liquid of specific gravity 3.36. Find the volume of the box, in m³.

Answer 1

mass of the box. m=308kg

weight of the box, w=m*g

weight of the box in liquid, w'=623N

specific gravity of the liquid=3.36

rho_liquid/rho_water=3.36

rho_liquid/(1000)=3.36

rho_liquid=3360 kg/m^3

here,

density of the box is, rho=m*g*rho_liquid/(m*g-w)

use,

rho_box*w-rho_box*w'=rho_liquid*m*g

rho_box*m*g-rho_box*w'=rho_liquid*m*g

rho_box*308*9.8-rho_box*623=3360*308*9.8

=====> rho_box=4233.87 kg/m^3

now volume of the box, V_box=m_box/rho_box

=308/(4233.87)

=0.073 m^3