JEE Mains · Physics · STD 11- 8. mechanical properties of solids
Four identical hollow cylindrical columns of mild steel support a big structure of mass \(50 \times 10^{3} {kg}\), The inner and outer radii of each column are \(50\; {cm}\) and \(100 \;{cm}\) respectively. Assuming uniform local distribution, calculate the compression strain of each column. [Use \(\left.{Y}=2.0 \times 10^{11} \;{Pa}, {g}=9.8\; {m} / {s}^{2}\right]\)
- A \(3.60 \times 10^{-8}\)
- B \(2.60 \times 10^{-7}\)
- C \(1.87 \times 10^{-3}\)
- D \(7.07 \times 10^{-4}\)
Answer & Solution
Correct Answer
(B) \(2.60 \times 10^{-7}\)
Step-by-step Solution
Detailed explanation
Force on each column \(=\frac{{mg}}{4}\) \(\text { Strain } =\frac{{mg}}{4 {AY}}\) \(=\frac{50 \times 10^{3} \times 9.8}{4 \times \pi(1-0.25) \times 2 \times 10^{11}}\) \(=2.6 \times 10^{-7}\)
See the Complete Solution
Get step-by-step explanations for this and 2.5 Lakh+ more JEE, NEET & CET questions.
- Unlock all solutions
- Practice the full chapter
- Track accuracy across PYQs
4.8 rated on Google Play · 14,000+ reviews
More questions from Physics
- Match the LIST-I with LIST-II
LIST-I LIST-II (A) Boltzmann constant I. \(\mathrm{ML}^2 \mathrm{~T}^{-1}\) (B) Coefficient of viscosity II. \(\mathrm{MLT}^{-3} \mathrm{~K}^{-1}\) (C) Planck's constant III. \(\mathrm{ML}^2 \mathrm{~T}^{-2} \mathrm{~K}^{-1}\) (D) Thermal conductivity IV. \(\mathrm{ML}^{-1} \mathrm{~T}^{-1}\)
Choose the correct answer from the options given below :JEE Mains 2025 Medium - A current through a wire depends on time as \(i =\alpha_{0} t +\beta t ^{2}\) where \(\alpha_{0}=20 A / s\) and \(\beta=8 As ^{-2} .\) Find the charge crossed through a section of the wire in \(15 \,s\) (in \(C\))JEE Mains 2021 Medium
- If \(‘M’\) is the mass of water that rises in a capillary tube of radius \(‘r’,\) then mass of water which will rise in a capillary tube of radius \(‘2r’\) isJEE Mains 2019 Medium
- Intensity of sunlight is observed as \(0.092\, {Wm}^{-2}\) at a point in free space. What will be the peak value of magnetic field at that point? \(\left(\sigma_{0}=8.85 \times 10^{-12}\, {C}^{2} \,{N}^{-1} \,{m}^{-2}\right.\) )JEE Mains 2021 Medium
- The radius in kilometer to which the present radius of earth \(( R =6400\, km )\) to be compressed so that the escape velocity is increased \(10\) time is ............\(km\)JEE Mains 2021 Medium
- For a hydrogen atom, the ratio of the largest wavelength of Lyman series to that of the Balmer series is _______.JEE Mains 2025 Easy
More PYQs from JEE Mains
- If \((a, b, c)\) is the image of the point \((1,2,-3)\) in the line, \(\frac{x+1}{2}=\frac{y-3}{-2}=\frac{z}{-1},\) then \(a+b+c\) is equal toJEE Mains 2020 Medium
- If the equation, \(x^{2}+b x+45=0(b \in R)\) has conjugate complex roots and they satisfy \(|z+1|=2 \sqrt{10},\) thenJEE Mains 2020 Hard
- A thin ring of \(10\, cm\) radius carries a uniformly distributed charge. The ring rotates at a constant angular speed of \(40\,\pi \,rad\,{s^{ - 1}}\) about its axis, perpendicular to its plane. If the magnetic field at its centre is \(3.8 \times {10^{ - 9}}\,T\), then the charge carried by the ring is close to \(\left( {{\mu _0} = 4\pi \times {{10}^{ - 7}}\,N/{A^2}} \right)\)JEE Mains 2019 Medium
- If two vertices of an equilateral triangle are \(A (- a, 0)\) and \(B ( a, 0),\,a > 0,\) and the third vertex \(C\) lies above \(x-\) axis then the equation of the circumcircle of \(\Delta ABC\) isJEE Mains 2013 Hard
- In the hydrogen atom, the electron makes a transition from the higher orbit (\(i\)) to a lower orbit (\(f\)). The ratio of the radius of the orbits in given by \(r_i : r_f = 16 : 4\). The wavelength of photon emitted due to this transition is _____ nm.
(Given Rydberg constant \(= 1.0973 \times 10^7\) /m)JEE Mains 2026 Hard - Two identical capacitors have same capacitance \(C\). One of them is charged to the potential \(\mathrm{V}\) and other to the potential \(2 \mathrm{~V}\). The negative ends of both are connected together. When the positive ends are also joined together, the decrease in energy of the combined system is _______.JEE Mains 2024 Hard