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JEE Main 20203 SeptemberEvening Shift
Exam
JEE Main
Year
2020
Date
3 September
Shift
Evening Shift
Subject
Physics
Chapter
Thermal Properties of Matter

JEE Main 2020 · 3 September · Evening Shift · Physics · Thermal Properties of Matter

A metallic sphere cools from 50 ° C to 40 ° C in 300s . If...

A metallic sphere cools from 50°C50 ° C to 40°C40 ° C in 300s300s. If atmospheric temperature around is 20°C20 ° C, then the sphere's temperature after the nest 55 minutes will be close to:

Options

  1. A31°C31 ° C
  2. B33°C33 ° C
  3. C28°C28 ° C
  4. D35°C35 ° C

Correct answer

B. 33°C33 ° C

Step-by-step solution

Using Newton's Law of cooling

50−405min=K(50+402−20)\dfrac{50 - 40}{5min} = K\left(\dfrac{50 + 40}{2} - 20\right) ......(i)

Next 5min.5min .

40−θ5=K(40+θ2−20)\dfrac{40 - \theta}{5} = K\left(\dfrac{40 + \theta}{2} - 20\right) .....(ii)

Dividing (ii)/(i)

40−θ10=40+θ−4050+40−40=θ50\dfrac{40 - \theta}{10} = \dfrac{40 + \theta - 40}{50 + 40 - 40} = \dfrac{\theta}{50}

40−θ=θ540 - \theta = \dfrac{\theta}{5}

200−5θ=θ200 - 5\theta = \theta

∴θ=2006=33.3°C∴ \theta = \dfrac{200}{6} = 33 . 3 ° C

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