If T = 2 pi sqrt{frac{L}{g}},where g is a con | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(C) Given the formula $T = 2 \pi \sqrt{\frac{L}{g}}$.Taking the natural logarithm on both sides: $\ln T = \ln(2 \pi) + \frac{1}{2} \ln L - \frac{1}{2}

Vedclass · Accepted Answer

$200$

Vedclass · Answer

(C) Given the formula $T = 2 \pi \sqrt{\frac{L}{g}}$.Taking the natural logarithm on both sides: $\ln T = \ln(2 \pi) + \frac{1}{2} \ln L - \frac{1}{2} \ln g$.Differentiating both sides,we get $\frac{dT}{T} = \frac{1}{2} \frac{dL}{L}$.The relative error in $T$ is $\frac{dT}{T}$.The percentage error in $L$ is $\frac{dL}{L} 	imes 100$.According to the problem,$\frac{dT}{T} = k 	imes (\frac{dL}{L} 	imes 100)$.Comparing this with $\frac{dT}{T} = \frac{1}{2} \frac{dL}{L}$,we have $k 	imes 100 = \frac{1}{2}$.Therefore,$k = \frac{1}{200}$.Thus,$\frac{1}{k} = 200$.

If $T = 2 \pi \sqrt{\frac{L}{g}}$,where $g$ is a constant and the relative error in $T$ is $k$ times the percentage error in $L$,then $\frac{1}{k} =$

Similar Questions

If $y=a \sin x+b \cos x$,then $y^2+\left(\frac{d y}{d x}\right)^2$ is a

$(1+\Delta)^{n} f(a)$ is equal to

If $f(x) = \frac{x}{1+x}$ and $g(x) = f(f(x))$,then $g^{\prime}(x)$ is equal to

If $y = x \sin x$ and $\frac{\frac{dy}{dx} - \frac{y}{x}}{x \frac{dy}{dx} - y}$ at $x = \alpha$ is $1$,then $\alpha =$

If $f(x)$ has a derivative at $x = a,$ then $\mathop {\lim }\limits_{x \to a} \frac{xf(a) - af(x)}{x - a}$ is equal to

Vedclass Test Series

Exam Paper Generator

Online Exam Module