Question

When a body floats in water ${\left(\frac{1}{3}\right)}^{rd}$ of its volume remains outside, whereas ${\left(\frac{3}{4}\right)}^{th}$ of its volume remains outside when it floats in a liquid. The density of the liquid, in gm/cc, is

• A. 8/3
• B. 4/3
• C. 9/4
• D. 3/2

Answer 1

Answer: (A)

: Initially, weight of floating body = weight of water displaced $=volumeofwater\times density\times g$ $=\frac{2V}{3}\times 1\times g=\frac{2Vg}{3}$ In second case, weight of floating body = weight of liquid displaced = volume of liquid $\times$ density of liquid $\times g$ $=\frac{V}{4}dg$ $\therefore$ $\frac{Vdg}{4}=\frac{2Vg}{3}$ or $d=\frac{8}{3}gm/cc$