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Q.

A simple pendulum is being used to determine the value of gravitational acceleration ‘g’ at a certain place. The length of the pendulum is 20.0 cm known to 1mm accuracy and a stop watch with 1s resolution measures the time taken for 40 oscillations to be 50s. The accuracy in g is

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a

3.5%

b

5.5%

c

4.5%

d

2.4%

answer is C.

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Detailed Solution

T=2πlg​on squaring both sides​g=4π2lT2​on differentiating,​Δgg=Δll+2ΔTT=0.120+2×150=0.045 ⇒Δgg×100=0.045​ ×100        ∴%Δgg=4.5%
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A simple pendulum is being used to determine the value of gravitational acceleration ‘g’ at a certain place. The length of the pendulum is 20.0 cm known to 1mm accuracy and a stop watch with 1s resolution measures the time taken for 40 oscillations to be 50s. The accuracy in g is