Question

A body weight $200gm$ in air $180gm$ in a liquid and $175gm$ in water. The density of the material of the body is

• A. $8000kg/m^3$
• B. $800kg/m^3$
• C. $8kg/m^3$
• D. $none$

Answer 1

The correct option is B $800kg/m^3$

The body weighs $200gm$ in air then,

$200=mg$. ($m=$ mass)

And it weighs $175g$ in water ( density of water $=1g$ per cubic cm)

Then,

$175=200-(V\times 1\times g)$ ..........(1). ($V=$ volume of body , $g=$ acceleration due to gravity)

From (1) we get ,

$V=2.5cc$.

In unknown liquid (suppose its density be d )it weighs 180 then,

$180=200-(2.5\times d\times g)$.......(2)

From (2) we get density $d=0.8g$ per cc $=800kg/m^3$