A hollow sphere of external radius R and thic | vedclass

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(B) The density of the metal is $ho$. The density of water is $ho_w = 1 	ext{ g/cm}^3$ (or $1000 	ext{ kg/m}^3$).For the hollow sphere to float,

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$t \leq \frac{R}{3 \rho}$

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(B) The density of the metal is $ho$. The density of water is $ho_w = 1 	ext{ g/cm}^3$ (or $1000 	ext{ kg/m}^3$).For the hollow sphere to float, its weight must be less than or equal to the weight of the water displaced by the total volume of the sphere.The volume of the metal shell is $V_m = 4 \pi R^2 t$ (since $t \ll R$).The mass of the sphere is $m_s = V_m 	imes ho = 4 \pi R^2 t ho$.The volume of water displaced by the sphere is $V_w = \frac{4}{3} \pi R^3$.The mass of the displaced water is $m_w = V_w 	imes ho_w = \frac{4}{3} \pi R^3 	imes 1$ (assuming $ho$ is relative to water density).For floatation, $m_s \leq m_w$:$4 \pi R^2 t ho \leq \frac{4}{3} \pi R^3$Dividing both sides by $4 \pi R^2$:$t ho \leq \frac{R}{3}$$t \leq \frac{R}{3 ho}$

$A$ hollow sphere of external radius $R$ and thickness $t$ $(t \ll R)$ is made of a metal of density $\rho$. The sphere will float in water if:

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