A student uses a simple pendulum of exactly 1 m 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 st

Question

A student uses a simple pendulum of exactly 1 m 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? [2010]

Smart Achievers · Accepted Answer

(1, 3)

The length of the string of simple pendulum is exactly 1 m (given), therefore the error in length $Δ l = 0$ .

Further the possibility of error in measuring time is 1s in 40s as the least count of stop watch is 1s.

$∴$ $\frac{Δ t}{t} = \frac{Δ T}{T} = \frac{1}{40}$

$Time period T = \frac{total time}{no. of oscillations} = \frac{40}{20} = 2 s$

$∴$ $\frac{Δ T}{T} = \frac{1}{40} \Rightarrow \frac{Δ T}{2} = \frac{1}{40} \Rightarrow Δ T = 0.05 s$

$Now for measuring error in g$

$using, T = 2 π \sqrt{\frac{l}{g}} \Rightarrow T^{2} = 4 π^{2} \frac{l}{g} \Rightarrow g = 4 π^{2} \frac{l}{T^{2}}$

$∴$ $Percentage error in g$

$\frac{Δ g}{g} \times 100 = \frac{Δ l}{l} \times 100 + 2 \frac{Δ T}{T} \times 100$

$∴$ $\frac{Δ g}{g} \times 100 = 0 + 2 (\frac{1}{40}) \times 100 = 5 %$

Solution

Q.
A student uses a simple pendulum of exactly 1 m 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 [2010]

1 Error $Δ T$ in measuring $T$ , the time period, is 0.05 seconds

2 Error $Δ T$ in measuring $T$ , the time period, is 1 second

3 Percentage error in the determination of $g$ is 5%

4 Percentage error in the determination of $g$ is 2.5%

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Solution

Q. A student uses a simple pendulum of exactly 1 m 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 [2010]

1 Error ΔT in measuring T, the time period, is 0.05 seconds

2 Error ΔT in measuring T, the time period, is 1 second

3 Percentage error in the determination of g is 5%