An object suspended by a wire stretches it by $$10$$ mm. When object is immersed in a liquid the elongation in wire reduces by $$5/3mm$$. The ratio of relative density of the object and liquid is

Question

An  object suspended by a wire stretches it by $$10$$ mm. When object is immersed in  a liquid the elongation in wire reduces by $$5/3mm$$. The ratio of relative  density of the object and liquid is

Infinity Learn · Accepted Answer

Given elongation $$e1=10$$ mm       $$e2=(10$$−$$53)$$ mm     Elongation $$e2=253mm$$     We know Young's modulus $$Y=FlAe$$...(1)     ⇒$$e1$$∝weight...(2)     ⇒$$e2$$∝ Apparent weight...(3)     $$equations(2)(3)$$⇒$$1010$$−$$53=MgMg$$−Mgρσ     ⇒$$55(22$$−$$13)=11$$−ρ$$6$$     ⇒$$65=11$$−ρ$$6$$     ⇒$$1$$−ρ$$6=56$$     ⇒ρσ$$=1$$−$$56=16$$

An object suspended by a wire stretches it by 10 mm. When object is immersed in a liquid the elongation in wire reduces by 5/3mm. The ratio of relative density of the object and liquid is

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