The weight of a body in water is one third of its weight in air. What is the density of the material of the body? Thanks

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Answer 1 · 2016-12-22T11:48:05

Let the volume of the body be #vcm^3#

the density of the body be #dgcm^-3#

So weight of the body in air#W_"air"=vdg# dyne,

#"where "g->"acceleration due to gravity"#

Now the bouyant force on the body when it is completely imerssed is the weight of displaced water

#W_"bouyant"=vxx1xxg# dyne.

Now the weight of the body in water

#W_"water"=W_"air"-W_"buoyant"=vg(d-1)# dyne

By the given condition

#W_"water"=1/3W_"air"#

#=>vg(d-1)=1/3vdg#

#=>d-1=1/3d#

#=>d-d/3=1#

#=>(2d)/3=1#

#=>d=3/2=1.5gcm^"-3"#