A person measures the depth of a well by meas | vedclass

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

Question

(B) The total time $T$ taken is the sum of the time taken by the stone to fall $(t_1)$ and the time taken by the sound to travel back $(t_2)$.$T = t_1

Vedclass · Accepted Answer

$1$

Vedclass · Answer

(B) The total time $T$ taken is the sum of the time taken by the stone to fall $(t_1)$ and the time taken by the sound to travel back $(t_2)$.$T = t_1 + t_2 = \sqrt{\frac{2L}{g}} + \frac{L}{v}$Given $L = 20 \ m$,$g = 10 \ ms^{-2}$,and $v = 300 \ ms^{-1}$.Differentiating $T$ with respect to $L$:$\frac{dT}{dL} = \frac{1}{2} \sqrt{\frac{2}{gL}} + \frac{1}{v} = \frac{1}{\sqrt{2gL}} + \frac{1}{v}$Substituting the values:$\frac{dT}{dL} = \frac{1}{\sqrt{2 	imes 10 	imes 20}} + \frac{1}{300} = \frac{1}{20} + \frac{1}{300} = \frac{15+1}{300} = \frac{16}{300} \ s/m$Since $\delta T = 0.01 \ s$,we have $\delta L = \delta T / (dT/dL) = 0.01 	imes (300/16) = 3/16 \ m = 0.1875 \ m$.The fractional error is $\frac{\delta L}{L} = \frac{0.1875}{20} = 0.009375$.Percentage error = $0.009375 	imes 100 \% \approx 0.9375 \% \approx 1 \%$.

Similar Questions

Two resistances $60 \pm 0.36 \ \Omega$ and $30 \pm 0.09 \ \Omega$ are connected in parallel. The equivalent resistance is

The mass of an empty beaker is $(10.1 \pm 0.1) \, g$. When it is completely filled with a liquid,its mass becomes $(17.3 \pm 0.1) \, g$. What is the best value for the mass of the liquid within the possible limits of accuracy?

The mass of an object is measured as $225 \pm 0.05 \, g$. Find the percentage error in this measurement. (in $\%$)

What is the fractional error in $g$ calculated from $T = 2\pi \sqrt {l/g}$? Given fractional errors in $T$ and $l$ are $\pm x$ and $\pm y$ respectively?

The length and breadth of a rectangle are $(5.7 \pm 0.1) \text{ cm}$ and $(3.4 \pm 0.2) \text{ cm}$,respectively. Calculate the area of the rectangle with error limits.

Vedclass Test Series

Exam Paper Generator

Online Exam Module