Q. Two cylinders of same cross-section and length $L$ but made of two material of densitites $\rho_{1}$ and $\rho_{2}$ (in CGS units) are cemented together to form a cylinder of length$2\ L$. If the combination floats in water with a length $L/2$ above the surface of water and $\rho_{1} < \rho_{2}$, then
A) $\rho_{1} > 1$
B) $\rho_{1} < 3/4$
C) $\rho_{1} > 1/2$
D) $\rho_{1} > 3/4\ $
Explanation
(b) Mass of the cylinders$= \ AL(\rho_{1} + \rho_{2})$. As cylinders float with length $L/2$ outside the water, therefore length of cylinder inside the water$= 3L/2$. When cylinders are floating, then, weight of cylinder $=$ weight of water displaced by cylinder
So $AL\left( \rho_{1} + \rho_{2} \right)g = A(3L/2\ ) \times 1 \times g$
Or $\rho_{1} + \rho_{2} = 3/2\ $
As $\rho_{1} < \rho_{2}$, so $\rho_{1} < 3/4$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.