Question

A hollow sphere of external radius R and thickness t(<<R) is made of metal of density p. The sphere will float in water if (take density of water 1 g /cm3).
A. t<=R/p
B. t<=R/3p
C. t<=R/2p
D. t>=R/3p​

Answer 1

B. $t \leq \frac{R}{3 \rho}$ is correct answer

Explanation:

The density of material is $\rho$

The hollow sphere floats only when its weight is smaller than the weight of the water displaced by the volume of the sphere which states, mass of the sphere is smaller than that for the same volume of water.  

mass of spherical ball, $m_1 = 4\pi R^2\times t \times \rho$

mass of water having same volume, $m_2= \frac{4}{3}\pi R^3 \times \rho_g = \frac{4}{3} \rho R^3$

$\rho_g$ is the density of water $= \frac {1 kg}{m^3}$

For the floatation of sphere, $m_1 \leq m_2$

$4\pi R^2 \times t \times \rho \leq \frac{4}{3}\pi R^3$

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

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

Thus, B. $t \leq \frac{R}{3 \rho}$ is correct answer