To estimate âgâ(from g = 4π2(L/T2)) error in measurement of L is ±2 % and error in measurement of T is ±3 %. The error in estimated âg' will be-

Question

To estimate âgâ(from g = 4π2(L/T2)) error in measurement of L is ±2 % and error in measurement of T is ±3 %. The error in estimated âg' will be- (A) ±8 % (B) ±6 % (C) ±3 % (D) ±5 %

Tardigrade Admin · Accepted Answer

g=4π2(L/T2) (Δ L/L)=±2 %=±2×10-2 (Δ T/T)=±3 %=±3×10-2 ⇒ (Δ g/g)=(Δ L/L)+(2Δ T/T) =2×10-2+2×3×10-2 =8×10-2=±8 %

Q. To estimate $‘ g ’$ (from $g = 4 π^{2} \frac{L}{T ^{2}})$ error in measurement of $L$ is $\pm 2%$ and error in measurement of $T$ is $\pm 3%$ . The error in estimated $‘ g^{'}$ will be-

$\pm 8%$

$\pm 6%$

$\pm 3%$

$\pm 5%$

$g = 4 π^{2} \frac{L}{T ^{2}}$

$\frac{Δ L}{L} = \pm 2% = \pm 2 \times 1 0^{- 2}$

$\frac{Δ T}{T} = \pm 3% = \pm 3 \times 1 0^{- 2}$

$\Rightarrow \frac{Δ g}{g} = \frac{Δ L}{L} + \frac{2Δ T}{T}$
$= 2 \times 1 0^{- 2} + 2 \times 3 \times 1 0^{- 2}$

$= 8 \times 1 0^{- 2} = \pm 8%$

Q. To estimate ‘g’(from g=4π2T2L​) error in measurement of L is ±2% and error in measurement of T is ±3%. The error in estimated ‘g′ will be-

±8%

±6%

±3%

±5%