A solid has a mass 39kg it loses 1/3 rd of its weight when immersed in water its volume will be
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Assume the volume of the body = v cm³ and the density of the body = d gcm⁻³.
The weight of the body in air, Wair = vdg dyne, where g is the acceleration due to gravity.
The buoyant force on the body when it is completely immersed is the weight of displaced water, Wbouyant = v x 1 x g dyne.
The weight of the body in water, Wwater = Wair - Wbuoyant = vg(d−1) dyne
According to the question, Wwater = 1/3 Wair
⇒vg(d−1) = 1/3 vdg
⇒d−1 = 1/3 d
⇒d−d/3 = 1
⇒2d/3 = 1
⇒d=3/2 = 1.5 gcm⁻³.
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