A hollow spherical shell of outer radius R fl | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(B) For the shell to float just submerged,the weight of the shell must be equal to the weight of the water displaced.Weight of shell = $V_{material} \

Vedclass · Accepted Answer

$0.88$

Vedclass · Answer

(B) For the shell to float just submerged,the weight of the shell must be equal to the weight of the water displaced.Weight of shell = $V_{material} 	imes ho_{material} 	imes g = \frac{4}{3} \pi (R^3 - r^3) ho_{material} g$.Weight of displaced water = $V_{total} 	imes ho_{water} 	imes g = \frac{4}{3} \pi R^3 ho_{water} g$.Equating the two: $\frac{4}{3} \pi (R^3 - r^3) ho_{material} g = \frac{4}{3} \pi R^3 ho_{water} g$.$(R^3 - r^3) ho_{material} = R^3 ho_{water}$.Given specific gravity $\frac{ho_{material}}{ho_{water}} = \frac{27}{8}$.So,$(R^3 - r^3) \frac{27}{8} = R^3$.$R^3 - r^3 = \frac{8}{27} R^3$.$r^3 = R^3 - \frac{8}{27} R^3 = \frac{19}{27} R^3$.$r = R \left( \frac{19}{27} ight)^{1/3} = \frac{R}{3} (19)^{1/3}$.Since $(19)^{1/3} \approx 2.668$,$r \approx \frac{2.668}{3} R \approx 0.889 R$.

$A$ hollow spherical shell of outer radius $R$ floats just submerged under the water surface. The inner radius of the shell is $r$. If the specific gravity of the shell material is $\frac{27}{8}$ with respect to water,the value of $r$ is $......R$.

Similar Questions

$A$ hollow sphere has an inner volume equal to half of its outer volume. If $4/5$ of its volume is submerged when placed in water,what is the density of the material of the sphere? (Density of water = $10^3 \ kg/m^3$)

$A$ body is suspended by a light string. The tensions in the string when the body is in air,when the body is totally immersed in water,and when the body is totally immersed in a liquid are respectively $40.2 \,N$,$28.4 \,N$,and $16.6 \,N$. The density of the liquid is

$A$ right circular cylinder has a mass $m$,radius $r$,and a height $h$. The cylinder is completely submerged in a fluid of density $\rho$,as shown in the diagram,and is released. What is the magnitude of the net force on the cylinder initially?

$A$ streamlined body falls through air from a height $h$ on the surface of a liquid. If $d$ and $D$ $(D > d)$ represent the densities of the material of the body and the liquid respectively,then the time after which the body will be instantaneously at rest is:

Consider a solid sphere of radius $R$ and mass density $\rho(r) = \rho_{0} \left(1 - \frac{r^{2}}{R^{2}}\right)$ for $0 < r \leq R$. The minimum density of a liquid in which it will float is

Vedclass Test Series

Exam Paper Generator

Online Exam Module