The period of oscillation of a simple pendulum is T = 2 π l g . Measured value of l is 20 . 0 cm , known to 1 mm accuracy and time for 100 oscillations of the pendulum is found to be 90 s using a wristwatch 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 l g . Measured value of l is 20 . 0 cm , known to 1 mm accuracy and time for 100 oscillations of the pendulum is found to be 90 s using a wristwatch of 1 s resolution. The accuracy in the determination of g is, 5 %, 4 %, 3 %, 1 %

MARKS App · Accepted Answer

∴ T = 2 π l g ⇒ g = 4 π 2 l T 2 ∴ Error in g can be calculated as Δ g g = Δ l l + 2 Δ T T . ∴ Total time for n oscillation is t = n T where T = time for oscillation. ⇒ Δ t t = Δ T T ⇒ Δ g g = Δ l l + 2 Δ t t Given that Δ l = 1 mm = 10 - 3 m , l = 20 × 10 - 2 m Δ t = 1 s , t = 90 s . % e r r o r i n g is Δ g g × 100 = Δ l l + 2 Δ t t × 100 = 10 - 3 20 × 10 - 2 + 2 × 1 90 × 100 = 1 2 + 20 9 = 0.5 + 2.22 = 2.72 % ≅ 3 %

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