A thin uniform cylindrical shell,closed at bo | vedclass

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(A) Let $V_0$ be the outer volume of the shell and $V_i$ be the inner volume of the shell.Let $V$ be the volume of water inside the shell.Let $\rho_c$

Vedclass · Accepted Answer

more than half filled if $\rho_c < 0.5$

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(A) Let $V_0$ be the outer volume of the shell and $V_i$ be the inner volume of the shell.Let $V$ be the volume of water inside the shell.Let $\rho_c$ be the relative density of the shell material.For the shell to float in a half-submerged state,the total weight of the shell and the water inside must equal the buoyant force exerted by the displaced water.The weight of the shell is $W_s = \rho_c (V_0 - V_i) g$.The weight of the water inside is $W_w = V g$.The buoyant force is $F_B = \frac{V_0}{2} g$ (since it is half-submerged).Equating weight and buoyant force: $\rho_c (V_0 - V_i) g + V g = \frac{V_0}{2} g$.Simplifying,we get: $\rho_c (V_0 - V_i) = \frac{V_0}{2} - V$.Thus,$\rho_c = \frac{V_0/2 - V}{V_0 - V_i}$.If $\rho_c Multiplying both sides by $2(V_0 - V_i)$ (assuming $V_0 > V_i$): $V_0 - 2V This simplifies to $-2V  V_i / 2$.Since $V$ is the volume of water and $V_i$ is the total inner volume,$V > V_i / 2$ means the shell is more than half filled.

$A$ thin uniform cylindrical shell,closed at both ends,is partially filled with water. It is floating vertically in water in a half-submerged state. If $\rho_c$ is the relative density of the material of the shell with respect to water,then the correct statement is that the shell is

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