Question

A homogeneous solid cylinder of length L$L / 4$ in the denser liquid as shown in the fig. The lower density liquid is open to atmosphere having pressure $P _ { 0 }$. Then density D of solid is given by

• A. $\frac { 5 } { 4 } d$
• B. $\frac { 4 } { 5 } d$
• C.
• D. $\frac { d } { 5 }$

Answer 1

Answer: (A)

$\frac { 5 } { 4 } d$

Answer 2

Weight of cylinder = upthrust due to both liquids

$V \times D \times g = \left( \frac { A } { 5 } \cdot \frac { 3 } { 4 } L \right) \times d \times g + \left( \frac { A } { 5 } \cdot \frac { L } { 4 } \right) \times 2 d \times g$

⇒ $\left( \frac { A } { 5 } \cdot L \right) D \cdot g = \frac { A L d g } { 4 }$⇒ $\frac { D } { 5 } = \frac { d } { 4 }$ $\therefore D = \frac { 5 } { 4 } d$