A person measures the depth of a well by measuring the time interval between dropping a stone and receiving the sound of impact with the bottom of the well. The error in his measurement of time is $\delta T =0.01$ seconds and he measures the depth of the well to be $L =20$ meters. Take the acceleration due to gravity $g =10\, ms ^{-2}$ and the velocity of sound is $300\, ms ^{-1}$. Then the fractional error in the measurement, $\delta L / L$, is closest to
- $0.2\%$
- $1\%$
- $3\%$
- $5\%$
The Correct Option is B
Solution and Explanation
The duration required for the stone to reach the ground.
\(t=\sqrt{\frac{2 L}{g}}+\frac{L}{C}\)
Here,C represents the speed of sound.
Now, differentiating the above equation
\(\frac{d t}{d L}=\sqrt{\frac{L}{g}} \times \frac{1}{2 \sqrt{L}}+\frac{1}{C}\)
\(dL =\frac{ dt }{\frac{1}{\sqrt{2 gL }}+\frac{1}{ C }}\)
We hat dt=0.01
\(\Rightarrow \frac{ dL }{ L } \times 100=\left(\frac{ dt }{\frac{1}{\sqrt{2 gL }}+\frac{1}{ C }}\right) \frac{1}{ L } \times 100\)
\(=\frac{15}{16 \%} \approx 1 \%\)
Top Questions on physical world
Match Column-I with Column-II related to an electric dipole of dipole moment \( \vec{p} \) that is placed in a uniform electric field \( \vec{E} \):
- KCET - 2025
- Physics
- physical world
- Which of the following statements is not true?
- KCET - 2025
- Physics
- physical world
- The particular solution of the differential equation, \[ x y \frac{dy}{dx} = x^2 + 2y^2 \quad \text{when} \quad y(1) = 0 \quad \text{is:} \]
- MHT CET - 2025
- Physics
- physical world
- If y = tan-1 ((2 + 3x) / (3 - 2x)) + tan-1 (4x / (1 + 5x2)), thendy/dx =
- MHT CET - 2025
- Physics
- physical world
- The area enclosed between the parabola \( y^2 = 4x \) and the line \( y = 2x - 4 \) is:
- MHT CET - 2025
- Physics
- physical world
Questions Asked in JEE Advanced exam
- Let $ x_0 $ be the real number such that $ e^{x_0} + x_0 = 0 $. For a given real number $ \alpha $, define $$ g(x) = \frac{3xe^x + 3x - \alpha e^x - \alpha x}{3(e^x + 1)} $$ for all real numbers $ x $. Then which one of the following statements is TRUE?
- JEE Advanced - 2025
- Fundamental Theorem of Calculus
- A linear octasaccharide (molar mass = 1024 g mol$^{-1}$) on complete hydrolysis produces three monosaccharides: ribose, 2-deoxyribose and glucose. The amount of 2-deoxyribose formed is 58.26 % (w/w) of the total amount of the monosaccharides produced in the hydrolyzed products. The number of ribose unit(s) present in one molecule of octasaccharide is _____.
Use: Molar mass (in g mol$^{-1}$): ribose = 150, 2-deoxyribose = 134, glucose = 180; Atomic mass (in amu): H = 1, O = 16- JEE Advanced - 2025
- Biomolecules
Let $ P(x_1, y_1) $ and $ Q(x_2, y_2) $ be two distinct points on the ellipse $$ \frac{x^2}{9} + \frac{y^2}{4} = 1 $$ such that $ y_1 > 0 $, and $ y_2 > 0 $. Let $ C $ denote the circle $ x^2 + y^2 = 9 $, and $ M $ be the point $ (3, 0) $. Suppose the line $ x = x_1 $ intersects $ C $ at $ R $, and the line $ x = x_2 $ intersects $ C $ at $ S $, such that the $ y $-coordinates of $ R $ and $ S $ are positive. Let $ \angle ROM = \frac{\pi}{6} $ and $ \angle SOM = \frac{\pi}{3} $, where $ O $ denotes the origin $ (0, 0) $. Let $ |XY| $ denote the length of the line segment $ XY $. Then which of the following statements is (are) TRUE?
- JEE Advanced - 2025
- Conic sections
- Adsorption of phenol from its aqueous solution on to fly ash obeys Freundlich isotherm. At a given temperature, from 10 mg g$^{-1}$ and 16 mg g$^{-1}$ aqueous phenol solutions, the concentrations of adsorbed phenol are measured to be 4 mg g$^{-1}$ and 10 mg g$^{-1}$, respectively. At this temperature, the concentration (in mg g$^{-1}$) of adsorbed phenol from 20 mg g$^{-1}$ aqueous solution of phenol will be ____. Use: $\log_{10} 2 = 0.3$
- JEE Advanced - 2025
- Adsorption
- At 300 K, an ideal dilute solution of a macromolecule exerts osmotic pressure that is expressed in terms of the height (h) of the solution (density = 1.00 g cm$^{-3}$) where h is equal to 2.00 cm. If the concentration of the dilute solution of the macromolecule is 2.00 g dm$^{-3}$, the molar mass of the macromolecule is calculated to be $X \times 10^{4}$ g mol$^{-1}$. The value of $X$ is ____. Use: Universal gas constant (R) = 8.3 J K$^{-1}$ mol$^{-1}$ and acceleration due to gravity (g) = 10 m s$^{-2}\}$
- JEE Advanced - 2025
- Colligative Properties
Concepts Used:
Physical World
The physical world includes the complications of the natural world around us. It is a type of analysis of the physical world around us to understand how it works. The fundamental forces that control nature are:
- Gravitational Force is a universal force that exists as an outcome of mutual attraction between any two objects with respect to their masses.
- Electromagnetic Force can be understood as the force that is present between the charged particles. The force is stated by Coulomb’s law.
- Strong Nuclear Force is the force that ties the protons and neutrons in a nucleus. Of all the elemental forces in nature, a strong nuclear force is the strongest as its name suggests.
- Weak Nuclear Force can only be noticed in some of the nuclear processes such as the beta decay of the nucleus.