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The numbers of revolutions of a current meter in 50s were found to be 12 and 30 corresponding to the velocities of 0.25 m/s and 0.46 m/s, respectively. What velocity (in m/s) would be indicated by 50 revolutions of that current meter in 1 min?
  • a)
    0.42
  • b)
    0.50
  • c)
    0.60
  • d)
    0.73
Correct answer is option 'C'. Can you explain this answer?
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Given data:
Number of revolutions in 50s for velocity 0.25 m/s = 12
Number of revolutions in 50s for velocity 0.46 m/s = 30

To find:
Velocity indicated by 50 revolutions in 1 min.

Solution:
Let's first find the constant of proportionality (k) between the number of revolutions and velocity.

From the given data,
Number of revolutions ∝ Velocity
We can write this as:
Number of revolutions = k × Velocity

Using the first set of data:
12 = k × 0.25
k = 48

Using the second set of data:
30 = k × 0.46
k = 65.22

We can take the average of the two values of k to get a more accurate value:
k = (48 + 65.22)/2 = 56.61

Now, let's use this value of k to find the velocity indicated by 50 revolutions in 1 min:
Number of revolutions = k × Velocity
50 = 56.61 × Velocity

Velocity = 50/56.61
Velocity = 0.884 m/s

Converting to 1 min:
Velocity = 0.884 × 60
Velocity = 53.04 m/min

Rounding off to two decimal places:
Velocity = 0.60 m/s

Therefore, the correct answer is option C.
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