Question

19. The weight of a body in water is one third of its weight in air. The density of the body
(1) 0.5 g/cm3
(2) 1.5 g/cm3
(3) 2.5 g/cm
(4) 3.5 g/cm​

Answer 1

HERE IS YOUR ANSWER ☆

(2) 1.5 g/cm³

Let the volume of the body be vcm3

the density of the body be dgcm−3

So weight of the body in airWair=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

Wbouyant=v×1×g dyne.

Now the weight of the body in water

Wwater=Wair−Wbuoyant=vg(d−1) dyne

By the given condition

Wwater=13Wair

⇒vg(d−1)=13vdg

⇒d−1=13d

⇒d−d3=1

⇒2d3=1

d = 3/2

= 1.5g/ cm³

HOPE IT HELPS YOU!!