Question:
The velocity of upper layer of water in a river is \(36\ kmh^{–1}\). Shearing stress between horizontal layers of water is \(10^{–3} Nm^{–2}\). Depth of the river is ______ m. (Co-efficient of viscosity of water is \(10^{–2} Pa.s\))
The velocity of upper layer of water in a river is \(36\ kmh^{–1}\). Shearing stress between horizontal layers of water is \(10^{–3} Nm^{–2}\). Depth of the river is ______ m. (Co-efficient of viscosity of water is \(10^{–2} Pa.s\))
Updated On: Jul 8, 2024
Hide Solution
Verified By Collegedunia
Correct Answer: 100
Solution and Explanation
We know that,
\(F = -ηA\frac {du}{dx}\)
\(10^{-3} = 10^{-2} \times \frac {10}{h}\)
\(h =\frac {10^{-1}}{10^{-3}}\)
\(h = 100\ m\)
So, the answer is \(100 \ m\).
Was this answer helpful?
0
0
Top Questions on Stress and Strain
- For smaller deformations, stress is directly proportional to the strain for any material. Then the constant of proportionality is called as its
- KEAM - 2025
- Physics
- Stress and Strain
- One end of a steel wire is fixed to the ceiling of an elevator moving up with an acceleration \( 2 \, \text{m/s}^2 \) and a load of 10 kg hangs from the other end. If the cross-section of the wire is \( 2 \, \text{cm}^2 \), then the longitudinal strain in the wire will be (Take \( g = 10 \, \text{m/s}^2 \) and \( Y = 2.0 \times 10^{11} \, \text{N/m}^2 \)).
- WBJEE - 2025
- Physics
- Stress and Strain
- Young's modulus and shear modulus are applicable for:
- KEAM - 2025
- Physics
- Stress and Strain
- The total energy of a satellite in a circular orbit at a distance \( (R + h) \) from the center of the Earth varies as
- KCET - 2025
- Physics
- Stress and Strain
- Two blocks of mass \(2 \, \text{kg}\) and \(4 \, \text{kg}\) are connected by a metal wire going over a smooth pulley as shown in the figure. The radius of the wire is \(4.0 \times 10^{-5} \, \text{m}\) and Young's modulus of the metal is \(2.0 \times 10^{11} \, \text{N/m}^2\). The longitudinal strain developed in the wire is \(\frac{1}{\alpha \pi}\). The value of \(\alpha\) is _____. [Use \(g = 10 \, \text{m/s}^2\)]
- JEE Main - 2024
- Physics
- Stress and Strain
View More Questions
Questions Asked in JEE Main exam
A conducting bar moves on two conducting rails as shown in the figure. A constant magnetic field \( B \) exists into the page. The bar starts to move from the vertex at time \( t = 0 \) with a constant velocity. If the induced EMF is \( E \propto t^n \), then the value of \( n \) is _____.
- JEE Main - 2025
- Magnetic Field
- Concentrated nitric acid is labelled as 75%by mass. The volume in mL of the solution which contains 30 g of nitric acid is: Given: Density of nitric acid solution is 1.25 g/mL.
- JEE Main - 2025
- Solutions
- A physical quantity \( Q \) is related to four observables \( a \), \( b \), \( c \), and \( d \) as follows: \[ Q = \frac{a b^4}{c d^2} \] Where:
- \( a = (60 \pm 3) \, \text{Pa} \),
- \( b = (20 \pm 0.1) \, \text{m} \),
- \( c = (40 \pm 0.2) \, \text{N·s/m}^2 \),
- \( d = (50 \pm 0.1) \, \text{m} \).
Then the percentage error in \( Q \) is:- JEE Main - 2025
- Error analysis
- Let circle $C$ be the image of
$$ x^2 + y^2 - 2x + 4y - 4 = 0 $$
in the line
$$ 2x - 3y + 5 = 0 $$
and $A$ be the point on $C$ such that $OA$ is parallel to the x-axis and $A$ lies on the right-hand side of the centre $O$ of $C$.
If $B(\alpha, \beta)$, with $\beta < 4$, lies on $C$ such that the length of the arc $AB$ is $\frac{1}{6}$ of the perimeter of $C$, then $\beta - \sqrt{3}\alpha$ is equal to: - Assume a living cell with 0.9%(\(w/w\)) of glucose solution (aqueous). This cell is immersed in another solution having equal mole fraction of glucose and water. (Consider the data up to first decimal place only) The cell will:
- JEE Main - 2025
- osmosis
View More Questions
Concepts Used:
Mechanical Properties of Solids
Mechanical properties of solids intricate the characteristics such as the resistance to deformation and their strength. Strength is the ability of an object to resist the applied stress, to what extent can it bear the stress.
Therefore, some of the mechanical properties of solids involve:
- Elasticity: When an object is stretched, it changes its shape and when we leave, it retrieves its shape. Or we can say it is the property of retrieving the original shape once the external force is removed. For example Spring
- Plasticity: When an object changes its shape and never attains its original shape even when an external force is removed. It is the permanent deformation property. For example Plastic materials.
- Ductility: When an object is been pulled in thin sheets, wires or plates, it will be assumed that it has ductile properties. It is the property of drawing into thin wires/sheets/plates. For example Gold or Silver
- Strength: The ability to hold out applied stress without failure. Many types of objects have higher strength than others.