Two bodies are in equilibrium when suspended in water from the arms of balance. The mass of one body is 36 g and its density is `9 g// cm^3` If the mass of the other is 46 g, its density in `g//cm^3` is

Options

A. `(4)/(3)`
B. `(3)/(2)`
C. 3
D. 5

Answer

C

Explanation

Volume of one body`=(36)/(9)=4cm^3`
Volume of water displaced `=4cm^3`
Upthrust acting on the body`=`weight of water displaced `=(4cm^3)``(1g)/(cm^3)=4gwt`
Weight of this body in water`=36g-4g=32gwt`
To be in equilibrium when suspended in water, the weight of the other body should also be 32 g wt.
Clearly, upthrust on this body`=48gwt-32gwt=16gwt`
Volume of this body`=(16g)/((1g)/(cm^3))=16cm^3`
Density of the body`=(48g)/(16cm^3)=(3g)/(cm^3)`