The period of oscillation of a simple pendulum is given by T $$=$$ $$2$$$$π$$lg where l is about $$100$$ cm and is known to have $$1$$ mm accuracy. The period is about $$2$$ s. The time of $$100$$ oscillations is measured by a stop watch of least count $$0.1$$ s. The percentage error in g is

Question

The period of oscillation of a simple pendulum is given by T $$=$$ $$2$$$$π$$lg where l is about $$100$$ cm and is known to have $$1$$ mm accuracy. The period is about $$2$$ s. The time of $$100$$ oscillations is measured by a stop watch of least count $$0.1$$ s. The percentage error in g is

Infinity Learn · Accepted Answer

T $$=$$ $$2$$$$π$$lg      ⇒$$T2$$ $$=$$ $$4$$$$π$$$$2lg$$ ⇒ g $$=$$ $$4$$$$π$$$$2lT2Here$$ % error in l $$=$$ $$1$$ $$mm100$$ cm ×$$100$$ $$=$$ $$0.1100$$×$$100$$ $$=$$ $$0.1$$%and % error in T $$=$$ $$0.12$$×$$100$$×$$100$$ $$=$$ $$0.05$$%∴ % error in g $$=$$ % error in l $$+$$ $$2($$% error in $$T)$$                            $$=0.1+2(0.05)$$ %                            $$=0.2$$%

The period of oscillation of a simple pendulum is given by $T = 2 π \sqrt{\frac{l}{g}}$ where l is about 100 cm and is known to have 1 mm accuracy. The period is about 2 s. The time of 100 oscillations is measured by a stop watch of least count 0.1 s. The percentage error in g is

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The period of oscillation of a simple pendulum is given by T = 2πlg where l is about 100 cm and is known to have 1 mm accuracy. The period is about 2 s. The time of 100 oscillations is measured by a stop watch of least count 0.1 s. The percentage error in g is

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The period of oscillation of a simple pendulum is given by $T = 2 π \sqrt{\frac{l}{g}}$ where l is about 100 cm and is known to have 1 mm accuracy. The period is about 2 s. The time of 100 oscillations is measured by a stop watch of least count 0.1 s. The percentage error in g is