Question

Two cylinders of same cross-section and length $L$ but made of two materials of densities $d_1$ and $d_2$ are connected together to a 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. $\frac{3d}{2}<d_1$
• C. $\frac{3d}{4}<d_1$
• D. $d_1<\frac{1}{4}d$

Answer 1

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



As the combined cylinder is at rest, the net force acting on the system should be zero.

$\Rightarrow$ The net buoyant force = weight of the system

$\therefore d(L+\frac{L}{2})Ag=d_{1}LAg+d_{2}LAg$

$\Rightarrow d_1+d_2=\frac{3d}{2}$

But since $d_1<d_2$,

$\therefore d_1+d_1<\frac{3d}{2}$

$\Rightarrow d_1<\frac{3}{4}d$

Hence, option $\left(\text{A}\right)$ is correct.