A cube of external side length 10 cm has an | vedclass

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

Question

(C) Let the density of the outer portion be $\rho_1$. Then the density of the inner portion is $2\rho_1$.The volume of the inner cube is $V_{in} = 5^3

Vedclass · Accepted Answer

$\frac{32}{9} \ g/cm^3$

Vedclass · Answer

(C) Let the density of the outer portion be $ho_1$. Then the density of the inner portion is $2ho_1$.The volume of the inner cube is $V_{in} = 5^3 = 125 \ cm^3$.The volume of the outer portion is $V_{out} = 10^3 - 5^3 = 1000 - 125 = 875 \ cm^3$.The total mass of the cube is $M = (V_{in} 	imes 2ho_1) + (V_{out} 	imes ho_1) = (125 	imes 2ho_1) + (875 	imes ho_1) = 250ho_1 + 875ho_1 = 1125ho_1$.For the cube to just float in a liquid of density $ho_L = 2 \ g/cm^3$, the weight of the cube must equal the weight of the displaced liquid:$Mg = V_{total} 	imes ho_L 	imes g$$1125ho_1 = 1000 	imes 2$$1125ho_1 = 2000$$ho_1 = \frac{2000}{1125} = \frac{16}{9} \ g/cm^3$.The density of the inner portion is $2ho_1 = 2 	imes \frac{16}{9} = \frac{32}{9} \ g/cm^3$.

$A$ cube of external side length $10 \ cm$ has an inner cubical cavity of side length $5 \ cm$. The density of the inner portion is twice that of the outer portion. If this cube is just floating in a liquid of density $2 \ g/cm^3$, find the density of the inner portion.

Similar Questions

$A$ wooden cube floats in water when a $200\,g$ mass is placed on it. When the mass is removed,the cube rises by $2\,cm$ above the water level. The side of the cube is ......... $cm$.

$A$ beaker containing water is placed on the platform of a spring balance. The balance reads $1.5 \, kg$. $A$ stone of mass $0.5 \, kg$ and density $500 \, kg/m^3$ is immersed in water without touching the walls of the beaker. What will be the balance reading now?

The ratio of masses of a cubical block of wood and a chunk of concrete is $\frac{3}{5}$ so that the combination just floats with its entire volume submerged under water. If the specific gravity of wood is $0.5$,then the specific gravity of concrete will be:

$A$ solid sphere of density $\rho_s$ which is $\eta$ times lighter than water (density $\rho_w$) is suspended in a water tank by a string tied to its base as shown in the figure. If the mass of the sphere is $m$,then the tension in the string is given by:

$A$ cube of ice floats partly in water and partly in kerosene oil. Find the ratio of the volume of ice immersed in water to that in kerosene oil. (Specific gravity of kerosene oil $= 0.8$, specific gravity of ice $= 0.9$)

Vedclass Test Series

Exam Paper Generator

Online Exam Module