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Consider two hot bodies B1 and B2 which have temperatures 100°C and 80°C respectively at t = 0. The temperature of the surroundings is 40°C. The ratio of the respective rates of cooling R1 and R2 of these two bodies at t = 0 will be
  • a)
    R1 : R2 = 3 : 2
  • b)
    R1 : R2 = 5 : 4
  • c)
    R1 : R2 = 2 : 3
  • d)
    R1 : R2 = 4 : 5
Correct answer is option 'A'. Can you explain this answer?
Most Upvoted Answer
Consider two hot bodies B1 and B2 which have temperatures 100°C and 8...
Given:
- Temperature of body B1 = 100°C
- Temperature of body B2 = 80°C
- Temperature of surroundings = 40°C

To find:
The ratio of the respective rates of cooling R1 and R2 of these two bodies at t = 0

Solution:
The rate of cooling of a body is directly proportional to the temperature difference between the body and its surroundings. Mathematically, it can be written as:
Rate of cooling ∝ (Temperature of body - Temperature of surroundings)

Let's calculate the rates of cooling for bodies B1 and B2 separately:

Rate of cooling for body B1:
Temperature difference between body B1 and its surroundings at t = 0: (100 - 40) = 60°C
Rate of cooling for body B1 at t = 0: R1 = k1 * 60 (where k1 is a constant)

Rate of cooling for body B2:
Temperature difference between body B2 and its surroundings at t = 0: (80 - 40) = 40°C
Rate of cooling for body B2 at t = 0: R2 = k2 * 40 (where k2 is a constant)

To find the ratio of R1 and R2, we can divide the two equations:
R1/R2 = (k1 * 60) / (k2 * 40)

Since the constants k1 and k2 are the same for both bodies, we can simplify the equation:
R1/R2 = 60/40
R1/R2 = 3/2

Therefore, the ratio of the respective rates of cooling R1 and R2 at t = 0 is:
R1 : R2 = 3:2

Answer: Option A
Free Test
Community Answer
Consider two hot bodies B1 and B2 which have temperatures 100°C and 8...
Initially at t = 0
Rate of cooling (R) ∝ Fall in temperature of body (θ - θ0)
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Consider two hot bodies B1 and B2 which have temperatures 100°C and 80°C respectively at t = 0. The temperature of the surroundings is 40°C. The ratio of the respective rates of cooling R1 and R2 of these two bodies at t = 0 will bea)R1 : R2 = 3 : 2b)R1 : R2 = 5 : 4c)R1 : R2 = 2 : 3d)R1 : R2 = 4 : 5Correct answer is option 'A'. Can you explain this answer?
Question Description
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