The percentage error in the measurement of g is (. Given that g= 4 π^2 ~L ~T^2 , ~L=(10 ± 0.1) cm , T=(100 ± 1) s):

Correct answer: C. 3 \% Given: aligned g & = 4 π^2 L T^2 L & =(10 ± 0.1) cm, and T & =(100 ± 1) s aligned Hence, error in measurement of g is aligned (Δ g)/(g) & = Δ L L +2 Δ T T & =(0.1)/(10) × 100+2 × (1)/(100) × 100 & =3 \% aligned

NEET 2022

Exam: NEET
Year: 2022
Subject: Physics
Chapter: Mathematics in Physics

NEET 2022 · Physics · Mathematics in Physics

The percentage error in the measurement of g is (. Given that g= 4...

The percentage error in the measurement of

g

is \left(\right.

Given that

g=\frac{4 \pi^2 \mathrm{~L}}{\mathrm{~T}^2}, \mathrm{~L}=(10 \pm 0.1) \mathrm{cm}

,

\mathrm{T}=(100 \pm 1) \mathrm{s}):

Options

A $2 \%$
B $5 \%$
C $3 \%$
D $7 \%$

Correct answer

C. $3 \%$

Step-by-step solution

Given:

\begin{aligned} g & =\frac{4 \pi^2 \mathrm{ L}}{\mathrm{ T}^2} \\ \mathrm{ L} & =(10 \pm 0.1) \mathrm{cm}, \text{ and } \\ \mathrm{T} & =(100 \pm 1) \mathrm{s} \end{aligned}

Hence, error in measurement of

g

\begin{aligned} \frac{\Delta g}{g} & =\frac{\Delta \mathrm{L}}{\mathrm{L}}+2 \frac{\Delta \mathrm{T}}{\mathrm{T}} \\ & =\frac{0.1}{10} \times 100+2 \times \frac{1}{100} \times 100 \\ & =3 \% \end{aligned}

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