Question

Two cylinders of same cross-section and length $L$ but made of two different materials of densities $d_1$ and $d_2$ are cemented together to form a cylinder of length $2L$. The combination floats in a liquid of density $d$ with a length $\frac{L}{2}$ above the surface of the liquid. If $d_1<d_2$ then

• A. $d_1<\frac{3}{4}d$
• B. $\frac{d}{2}>d_1$
• C. $\frac{d}{4}>d_1$
• D. $d<d_1$

Answer 1

The correct option is A $d_1<\frac{3}{4}d$

From Archimedes principle ,
Net weight = upthrust
$(d_1+d_2)LAg=\frac{3}{2}LAdg$
$\Rightarrow (d_1+d_2)=\frac{3}{2}d$
$\because d_1<d_2$ we can say that , $d_1<\frac{3}{4}d$
Hence, option (a) is the correct answer.