Question

A hollow sphere of external radius R and the thickness t is made of a metal of density.the sphere will floatif

Answer 1

Answer:

sorry I didn't know the answer to tell you

Answer 2

hollow sphere floats if this equation satisfy $t \leq \frac{r}{3\rho}$  

Explanation:

The hollow sphere will float if its weight is less than the weight of the water displaced by the volume of the sphere. This shows that mass of the sphere is less than that for the same volume of water which is replaced by the volume of sphere .  

Now,

mass of spherical cell $M_{1} = \textrm{solid volume of the sphere}\times \textrm{density of the material}$

$M_{1} = 4\pi r^{2}t\rho$  

Where, $M_{1} =$ mass of the hollow sphere

$r =$ radius of the hollow sphere

 $\rho =$  density of the hollow sphere

$t =$ thickness of the hollow sphere

While the mass of water having same volume  

$M_{2} = \textrm{whole volume of the sphere}\times \textrm{density of the water}$

$M_{2} = \frac{4}{3}\pi r^{3}\rho_{w}$

For the floatation of sphere $M_{1}\leq M_{2}$

$4\pi r^{2}t\rho \leq \frac{4}{3}\pi r^{3}\rho_{w}$

⇒ $t\rho \leq \frac{r}{3}$      $\because \rho _{w} = 1 \frac{g}{cm_{3}}$

⇒ Thickness $t \leq \frac{r}{3\rho}$