SATHEE: General Physics Question 15

General Physics Question 15

Question 15

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 $1 s$ for this and records $40 s$ for 20 oscillations. For this observation, which of the following statement(s) is/are true?

(2010)

(a) Error $Δ T$ in measuring $T$ , the time period, is $0.05 s$

(b) Error $Δ T$ in measuring $T$ , the time period, is $1 s$

(c) Percentage error in the determination of $g$ is $5$

(d) Percentage error in the determination of $g$ is $2.5$

Numerical Value Based Questions

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Answer:

Correct Answer: 16. (a, c)

Solution:

$T = \frac{40 s}{20} = 2 s$

Further, $t = n T = 20 T$ or $Δ t = 20 Δ T$

$∴ \frac{Δ t}{t} = \frac{Δ T}{T}$ or $Δ T = \frac{T}{t} \cdot Δ t = \frac{2}{40} (1) = 0.05 s$

Further, $T = 2 π \sqrt{\frac{l}{g}}$ or $T \propto g^{- 1 / 2}$

$∴ \frac{Δ T}{T} \times 100 = - \frac{1}{2} \times \frac{Δ g}{g} \times 100$

or error in determination of $g$ is

$\begin{aligned} \frac{Δ g}{g} \times 100 & = - 200 \times \frac{Δ T}{T} & = - \frac{200 \times 0.05}{2} & = - 5 \end{aligned}$

$∴$ Correct options are (a) and (c).

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