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 $ =volume\text{ }of\text{ }water\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 $