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 \(10^{–2} Pa.s\))
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 \(100 \ m\).
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
- A body of weight \( W \) is suspended from the ceiling of a room through a chain of weight \( w \). The ceiling pulls the chain by a force.
- KEAM - 2024
- Physics
- Stress and Strain
Questions Asked in JEE Main exam
The motion of an airplane is represented by the velocity-time graph as shown below. The distance covered by the airplane in the first 30.5 seconds is km.
- JEE Main - 2025
- Kinematics
- A force \( \mathbf{F} = 2\hat{i} + b\hat{j} + \hat{k} \) is applied on a particle and it undergoes a displacement \( \mathbf{r} = \hat{i} - 2\hat{j} - \hat{k} \). What will be the value of \( b \), if the work done on the particle is zero?
- JEE Main - 2025
- Work and Energy
Which of the following statement is true with respect to H\(_2\)O, NH\(_3\) and CH\(_4\)?
(A) The central atoms of all the molecules are sp\(^3\) hybridized.
(B) The H–O–H, H–N–H and H–C–H angles in the above molecules are 104.5°, 107.5° and 109.5° respectively.
(C) The increasing order of dipole moment is CH\(_4\)<NH\(_3\)<H\(_2\)O.
(D) Both H\(_2\)O and NH\(_3\) are Lewis acids and CH\(_4\) is a Lewis base.
(E) A solution of NH\(_3\) in H\(_2\)O is basic. In this solution NH\(_3\) and H\(_2\)O act as Lowry-Bronsted acid and base respectively.
- JEE Main - 2025
- Molecular Orbital Theory
- The increase in pressure required to decrease the volume of a water sample by 0.2percentage is \( P \times 10^5 \, \text{Nm}^{-2} \). Bulk modulus of water is \( 2.15 \times 10^9 \, \text{Nm}^{-2} \). The value of \( P \) is ________________.
- JEE Main - 2025
- System of Particles & Rotational Motion
The velocity-time graph of an object moving along a straight line is shown in the figure. What is the distance covered by the object between \( t = 0 \) to \( t = 4s \)?
- JEE Main - 2025
- Kinetic Energy
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.