Two thermometer bulbs have radius r = 1.0 cm . One is spherical; the other is cylindrical with length L = 4.0 cm , including both end faces. Let R C and R S denote volume divided by surface area f

Question

Two thermometer bulbs have radius r = 1.0 cm . One is spherical; the other is cylindrical with length L = 4.0 cm , including both end faces. Let R C ​ and R S ​ denote volume divided by surface area for the cylinder and sphere respectively. Find R c ​ / R s ​ . A larger ratio means slower response.

TestHub · Accepted Answer

Sphere: V / S = r /3 = 0.333 cm . Cylinder: V = π r 2 L = 4 π , S = 2 π r L + 2 π r 2 = 10 π , so V / S = 0.40 cm . Ratio = 0.40/0.333 = 1.2. The cylinder holds more liquid per unit area, so it responds more slowly; the sphere is faster.

Physics - Heat & Thermo Question with Solution | TestHub

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