Question 337: Properties of Matter

Question

Two non-mixing liquids of densities $$\rho $$ and n$$\rho $$ (n > 1) are put in a container. The height of each liquid is h. A solid cylinder of length L and density d is put in this container. The cylinder floats with its axis vertical and length $$\rho $$L ($$\rho $$ < 1) in the denser liquid. The density d is equal to

Accepted Answer

According to Archimedes principle,
Weight of the cylinder = (upthrust)
1
+ (upthrust)
2
i.e.,   $$ALdg = \left( {1 - p} \right)LA\rho g + \left( {pLA} \right)n\rho g$$
$$ \Rightarrow d = \left( {1 - p} \right)\rho  + pn\rho $$
$$ = \rho  - p\rho  + np\rho $$
$$ = \rho  + \left( {n + 1} \right)p\rho $$
$$ = p\left[ {1 + (n - 1)p} \right]$$

Answer

$$\left\{ {2 + \left( {n - 1} \right)p} \right\}\rho $$

Answer

$$\left\{ {1 + \left( {n - 1} \right)p} \right\}\rho $$

Answer

$$\left\{ {1 + \left( {n + 1} \right)p} \right\}\rho $$

Answer

$$\left\{ {2 + \left( {n + 1} \right)p} \right\}\rho $$

Properties of Matter

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