Question

Two spheres of different materials, one with double the radius and one-fourth the thickness of the other, are filled with ice. If the time taken for complete melting of the larger sphere is 25 minutes and for the smaller one is 16 minutes, the ratio of thermal conductivities of the materials of the larger sphere to that of the smaller sphere is:

• A. \(4:5\)
• B. \(5:4\)
• C. \(25:8\)
• D. 8:25

Hint:

Melting time increases with thickness and decreases with thermal conductivity.

Answer 1

The Correct Option is B

Step 1: Heat flow rate: (Q)/(t) ∝ (kA)/(d)
Step 2: Time for melting: t ∝ (d)/(kA)
Step 3: Using given ratios and times: (kL)/(kS) = (tS)/(tL) · (dL)/(dS) · (AL)/(AS) = (16)/(25) · (1)/(4) · 4 = (5)/(4)