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In an experiment to determine the period of a simple pendulum of length 1 m, it is attached to different spherical bobs of radii r1 and r2. The two spherical bobs have uniform mass distribution. If the relative difference in the periods, is found to be 5×10−4 s, the difference in radii, |r1−r2| is best given by:
  • a)
    1 cm
  • b)
    0.1 cm
  • c)
    0.5 cm
  • d)
    0.01 cm
Correct answer is option 'B'. Can you explain this answer?
Most Upvoted Answer
In an experiment to determine the period of a simple pendulum of lengt...
To determine the period of a simple pendulum, we can use the formula:

T = 2π√(L/g)

Where:
T = period of the pendulum
L = length of the pendulum
g = acceleration due to gravity

In this experiment, the length of the pendulum is fixed at 1 m. Let's assume that the radii of the two spherical bobs are r1 and r2, respectively.

The relative difference in periods is given by:

ΔT/T = (T2 - T1)/T1

Where:
ΔT = difference in periods
T1 = period of the pendulum with bob of radius r1
T2 = period of the pendulum with bob of radius r2

We are given that the relative difference in periods is 5%, which can be expressed as:

5/100 = (T2 - T1)/T1

Rearranging the equation, we get:

(T2 - T1)/T1 = 0.05

Now, let's substitute the formula for the period of the pendulum into the equation:

(2π√(L2/g) - 2π√(L1/g))/(2π√(L1/g)) = 0.05

Simplifying the equation, we can cancel out the common terms:

√(L2/g) - √(L1/g) = 0.05√(L1/g)

Now, let's substitute the value of L (length of the pendulum) as 1 m:

√(1/g)(√(r2) - √(r1)) = 0.05√(1/g)

Simplifying the equation further, we get:

√(r2) - √(r1) = 0.05

Therefore, the relative difference in the radii of the two spherical bobs is 0.05.
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In an experiment to determine the period of a simple pendulum of length 1 m, it is attached to different spherical bobs of radii r1 and r2. The two spherical bobs have uniform mass distribution. If the relative difference in the periods, is found to be 5×10−4 s, the difference in radii,|r1−r2|is best given by:a)1 cmb)0.1 cmc)0.5 cmd)0.01 cmCorrect answer is option 'B'. Can you explain this answer?
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In an experiment to determine the period of a simple pendulum of length 1 m, it is attached to different spherical bobs of radii r1 and r2. The two spherical bobs have uniform mass distribution. If the relative difference in the periods, is found to be 5×10−4 s, the difference in radii,|r1−r2|is best given by:a)1 cmb)0.1 cmc)0.5 cmd)0.01 cmCorrect answer is option 'B'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about In an experiment to determine the period of a simple pendulum of length 1 m, it is attached to different spherical bobs of radii r1 and r2. The two spherical bobs have uniform mass distribution. If the relative difference in the periods, is found to be 5×10−4 s, the difference in radii,|r1−r2|is best given by:a)1 cmb)0.1 cmc)0.5 cmd)0.01 cmCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In an experiment to determine the period of a simple pendulum of length 1 m, it is attached to different spherical bobs of radii r1 and r2. The two spherical bobs have uniform mass distribution. If the relative difference in the periods, is found to be 5×10−4 s, the difference in radii,|r1−r2|is best given by:a)1 cmb)0.1 cmc)0.5 cmd)0.01 cmCorrect answer is option 'B'. Can you explain this answer?.
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