The period of oscillation of a simple pendulum is $$T=2$$$$π$$Lg. Measured value of L is $$20$$ cm known to $$1mm$$ accuracy and time for $$100$$ oscillations of the pendulum is found to be $$90$$ s using a $$wrist-watch$$ of $$1$$ s resolution. The accuracy in the determination of g is

Question

The period of oscillation of a simple  pendulum is $$T=2$$$$π$$Lg. Measured value of L is $$20$$ cm known to  $$1mm$$ accuracy and time for $$100$$ oscillations of the pendulum is found to be $$90$$ s using a $$wrist-watch$$ of $$1$$ s resolution. The accuracy in the determination of g is

Infinity Learn · Accepted Answer

Given, $$T=2$$$$π$$Lgor $$g=4$$$$π$$$$2LT2Hence$$, $$T=tn$$  and  Δ$$T=$$Δtn∴           Δ$$TT=$$ΔttThe errors in both L and t are the least count errors. Therefore, $$($$Δ$$gg)=($$Δ$$LL)+2($$Δ$$TT)=0.120.0+2(190)=0.027The$$ percentage error in g $$is($$Δ$$gg)$$×$$100=($$Δ$$LL)$$×$$100+2$$×$$($$Δ$$TT)$$×$$100=3$$%

The period of oscillation of a simple pendulum is $T = 2 π \sqrt{\frac{L}{g}} .$ Measured value of L is 20 cm known to 1mm accuracy and time for 100 oscillations of the pendulum is found to be 90 s using a wrist-watch of 1 s resolution. The accuracy in the determination of g is

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The period of oscillation of a simple pendulum is T=2πLg. Measured value of L is 20 cm known to 1mm accuracy and time for 100 oscillations of the pendulum is found to be 90 s using a wrist-watch of 1 s resolution. The accuracy in the determination of g is

Remember concepts with our Masterclasses.

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The period of oscillation of a simple pendulum is $T = 2 π \sqrt{\frac{L}{g}} .$ Measured value of L is 20 cm known to 1mm accuracy and time for 100 oscillations of the pendulum is found to be 90 s using a wrist-watch of 1 s resolution. The accuracy in the determination of g is