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Q.

The time period of oscillation of simple pendulum is given by T=2πlg where  l is 100 cm  and is known to have  0.1 cm accuracy. The time period is  2s. The time (t) of 100 oscillations is measured by a stop watch of least count 0.1s. The maximum percentage error in measurement of g is

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a

0.1%

b

0.2%

c

0.8%

d

1%

answer is B.

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Detailed Solution

GivenThe time period of simple pendulum T=2πlg⇒g=4π2lT2⇒Δgg=Δll+2ΔTTt=100T=200s⇒Δtt=ΔTT⇒Δgg=Δll+2⋅Δtt⇒Δgg=0.1100+20.11002⇒Δgg×100=0.2%
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The time period of oscillation of simple pendulum is given by T=2πlg where  l is 100 cm  and is known to have  0.1 cm accuracy. The time period is  2s. The time (t) of 100 oscillations is measured by a stop watch of least count 0.1s. The maximum percentage error in measurement of g is