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QJEEM17Phc5b3: JEE Main 2017 Physics - Class 11 JEEM17Phc5b3 Solution: In an experiment to determine the period of a simple pendulum…

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 :

Multiple Choice Options

  • A 1 cm
  • B 0.05 cm
  • C 0.5 cm
  • D 0.01 cm

Step-by-Step Verified Solution

The time period is given by the formula

T=2πlg

which clearly indicates that the time period is directly proportional to the length of the pendulum l, that is,

T∝l

Here, l = 1 m. Therefore,

ΔTl=12Δll ....... (1)

where Δl=|r1−r2|. Substituting the values in Eq. (1), we get

5×10−4=12(r1−r21)

⇒r1−r2=10×10−4=10−3 m =10−1 cm =0.1 cm

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