Two hollow spheres of same thickness are filled with ice. The ratio of their diameter is $1 : 2$ and the ratio of thermal conductivities of the materials is $2 : 3$ . The ratio of times in which the ice gets melted in the two spheres is :

3 : 4

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

4 : 3

No worries! We‘ve got your back. Try BYJU‘S free classes today!

3 : 8

No worries! We‘ve got your back. Try BYJU‘S free classes today!

8 : 3

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is D $3 : 4$
$\frac{d_{1}}{d_{2}} = \frac{1}{2} \Rightarrow \frac{r_{1}}{r_{2}} = \frac{1}{2} \frac{K_{1}}{K_{2}} = \frac{2}{3}$
Let in container1, $Q_{1}$ heat is required and in container2, $Q_{2}$ heat is required

Ratio of time taken to melt complete ice
$= \frac{\frac{Q_{1}}{h e a t_c u r r e n t 1}}{\frac{Q_{2}}{h e a t_c u r r e n t 2}}$

$= \frac{\frac{\frac{4}{3} π r_{1}^{3} \times ρ_{i c e} \times L_{f}}{\frac{△ Q \times k_{1} A_{1}}{l}}}{\frac{\frac{4}{3} π r_{2}^{3} \times ρ_{i c e} \times L_{f}}{\frac{△ Q \times k_{2} A_{2}}{l}}} = \frac{k_{2} A_{2} r_{1}^{3}}{k_{1} A_{1} r_{2}^{3}} = \frac{3 \times 4 \times 1}{2 \times 1 \times 8} = \frac{3}{4}$

Suggest Corrections

Similar questions

Q. Two hollow metal spheres with radii in the ratio

1 : 2

and ratio of thickness

2 : 3

are filled with ice. If the ratio of times taken for the ice to completely melt is

2 : 3

, the ratio of their thermal conductivities is :

Q. Two hollow spheres of same material one with double the radius of the other and double the thickness of the other filled with ice. The ratio of times in which ice gets melted in the two spheres is:

Two hollow spheres of different materials, one with double the radius and one-fourth wall thickness of the other, are filled with ice. If the times taken for complete melting of ice in the larger to the smaller one are in the ration of 25:16, then their corresponding thermal conductivities are in the ratio

Q. The radius and one-fourth wall thickness of the other are filled with ice. If the time taken for complete melting on ice in the larger sphere is

25

and for smaller one is

16

minute, the ratio to thermal conductivities of the materials of larger spheres to that of smaller sphere is

Q. There are two hollow spheres made of different materials, one with double the radius and one fourth wall thickness of the other are filled with ice. If the time taken for melting the ice completely in larger sphere is

25

minutes and that for smaller sphere is

16

minutes, the ratio of the thermal conductivity of the larger sphere to the smaller sphere is :

Join BYJU'S Learning Program

Two hollow spheres of same thickness are filled with ice. The ratio of their diameter is 1:2 and the ratio of thermal conductivities of the materials is 2:3. The ratio of times in which the ice gets melted in the two spheres is :

The correct option is D 3:4d1d2=12⇒r1r2=12K1K2=23Let in container1, Q1 heat is required and in container2, Q2heat is requiredRatio of time taken to melt complete ice=Q1heat_current1Q2heat_current2=43πr31×ρice×Lf△Q×k1A1l43πr32×ρice×Lf△Q×k2A2l=k2A2r31k1A1r32=3×4×12×1×8=34

Two hollow spheres of same thickness are filled with ice. The ratio of their diameter is $1 : 2$ and the ratio of thermal conductivities of the materials is $2 : 3$ . The ratio of times in which the ice gets melted in the two spheres is :