IIT-JEE 2010 · Paper 1 · Physics Q66

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PhysicsMultiple correct+3Question 66 of 84

A student uses a simple pendulum of exactly 1m length to determine g, the acceleration due to gravity. He uses a stop watch with the least count of 1 sec for this and records 40 seconds for 20 oscillations. For this observation, which of the following statement(s) is (are) true?

Error

\Delta T

in measuring T, the time period, is 0.05 seconds

Error

\Delta T

in measuring T, the time period, is 1 second

Percentage error in the determination of g is 5%

Percentage error in the determination of g is 2.5%

Answer and worked solution

Official answer: A, C

Period. $T=\dfrac{40}{20}=2$ s. The stopwatch error of 1 s is spread over 20 oscillations:
$\Delta T=\frac1{20}=0.05\text{ s}.$
(A) true, (B) false.

Error in g. $g=\dfrac{4\pi^2L}{T^2}$ with $L$ exact:
$\frac{\Delta g}g=2\frac{\Delta T}T=2\times\frac{0.05}2=5\%.$
(C) true, (D) false.

(A), (C)

Topics:Simple pendulum experiment Errors in measurement

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IIT-JEE 2010 · Paper 1, Physics question 66