Question:
A horizontal metal rod of diameter 4 cm projects 6 cm from a wall. The shear modulus of the metal is \(3 \times 10^{10}\, N\,m^{-2}\). An object of mass 1100 kg is suspended from the free end of the rod. The free end of the rod moves down by a distance. (Take \(g = 10\,m\,s^{-2}\), neglect mass of rod)
A horizontal metal rod of diameter 4 cm projects 6 cm from a wall. The shear modulus of the metal is \(3 \times 10^{10}\, N\,m^{-2}\). An object of mass 1100 kg is suspended from the free end of the rod. The free end of the rod moves down by a distance. (Take \(g = 10\,m\,s^{-2}\), neglect mass of rod)
Show Hint
For shear problems, always use \( \Delta x = \frac{FL}{AG} \) and carefully track powers of 10 in area.
Updated On: Jun 19, 2026
- \(2.5 \times 10^{-6}\, m\)
- \(6.75 \times 10^{-5}\, m\)
- \(2.25 \times 10^{-6}\, m\)
- \(1.75 \times 10^{-5}\, m\)
Show Solution
Verified By Collegedunia
The Correct Option is D
Solution and Explanation
Step 1: Identify given parameters.
Diameter \(d = 4\,cm = 0.04\,m\), so radius \(r = 0.02\,m\).
Length \(L = 6\,cm = 0.06\,m\).
Shear modulus \(G = 3 \times 10^{10}\,N\,m^{-2}\).
Force \(F = mg = 1100 \times 10 = 11000\,N\).
Step 2: Use shear strain formula.
For lateral displacement: \[ \Delta x = \frac{FL}{AG} \]
Step 3: Area of cross-section.
\[ A = \pi r^2 = \pi (0.02)^2 = 1.256 \times 10^{-3}\,m^2 \]
Step 4: Substitute values.
\[ \Delta x = \frac{11000 \times 0.06}{(1.256 \times 10^{-3})(3 \times 10^{10})} \]
Step 5: Simplify.
Numerator: \[ 11000 \times 0.06 = 660 \]
Denominator: \[ 3.768 \times 10^{7} \]
Step 6: Final result.
\[ \Delta x \approx 1.75 \times 10^{-5}\,m \]
Final Answer: \[ \boxed{1.75 \times 10^{-5}\,m} \]
Diameter \(d = 4\,cm = 0.04\,m\), so radius \(r = 0.02\,m\).
Length \(L = 6\,cm = 0.06\,m\).
Shear modulus \(G = 3 \times 10^{10}\,N\,m^{-2}\).
Force \(F = mg = 1100 \times 10 = 11000\,N\).
Step 2: Use shear strain formula.
For lateral displacement: \[ \Delta x = \frac{FL}{AG} \]
Step 3: Area of cross-section.
\[ A = \pi r^2 = \pi (0.02)^2 = 1.256 \times 10^{-3}\,m^2 \]
Step 4: Substitute values.
\[ \Delta x = \frac{11000 \times 0.06}{(1.256 \times 10^{-3})(3 \times 10^{10})} \]
Step 5: Simplify.
Numerator: \[ 11000 \times 0.06 = 660 \]
Denominator: \[ 3.768 \times 10^{7} \]
Step 6: Final result.
\[ \Delta x \approx 1.75 \times 10^{-5}\,m \]
Final Answer: \[ \boxed{1.75 \times 10^{-5}\,m} \]
Was this answer helpful?
0
0
Top AP EAPCET Physics Questions
- A body is projected from the ground at an angle of $\tan^{-1} \left( \frac{8}{7}\right)$ with the horizontal. The ratio of the maximum height attained by it to its range is
- A lens forms real and virtual images of an object, when the object is at $u_{1}$ and $u_{2}$ distances respectively. If the size of the virtual image is double that of the real image, then the focal length of the lens is (take, the magnification of the real image as $m$ )
- Two spheres $P$ and $Q$, each of mass $200\, g$ are attached to a string of length one metre as shown in the figure. The string and the spheres are then whirled in a horizontal circle about $O$ at a constant angular speed. The ratio of the tension in the string between $P$ and $Q$ to that of between $P$ and $O$ is $(P$ is at mid-point of the line joining $O$ and $Q$ )
- The radii of the two columns in a U - tube are r1 and r2. When a liquid of density p (angle of contact is $ 0{}^\circ $ ) is filled in it, the level difference of the liquid in the two arms is h. The surface tension of the liquid is: (g = acceleration due to gravity)
- A rigid metallic sphere is spinning around its own axis in the absence of external torque. If the temperature is raised, its volume increases by $9 \%$. The change in its angular speed is
View More Questions
Top AP EAPCET Stress and Strain Questions
- A light rod of length 100 cm is suspended from the ceiling horizontally by means of two vertical wires of equal lengths tied to the ends of the rod. One of the wires is made of steel and is of area of cross- section $ 0.1\text{ }c{{m}^{2}}. $ The other wire is of brass and of area of cross-section $ 0.2\text{ }c{{m}^{2}}. $ The position from the steel wire along the rod at which a load is to be placed to produce equal stresses in both wires is ( $ {{Y}_{steel}}=20\times {{10}^{11}} $ dyne $ c{{m}^{-2}};\text{ }({{Y}_{brass}}=10\times {{10}^{11}}dyne\text{ }c{{m}^{-2}}) $
- Two copper wires of length $L$ and $2L$ have radii $r$ and $2r$ respectively. If they are subjected to the same tension force, the ratio of their extension ($\Delta L_1 / \Delta L_2$) is:
- A piece of metal having a square cross section of area 400 mm\(^2\) is pulled with 40 kN force, producing only elastic deformation. If the Young's modulus of the metal is \(40 \times 10^9~\text{N/m}^2\), then the strain is:
Top AP EAPCET Questions
- A body is projected from the ground at an angle of $\tan^{-1} \left( \frac{8}{7}\right)$ with the horizontal. The ratio of the maximum height attained by it to its range is
- The four quantum numbers of the valence electron of potassium are :
- A lens forms real and virtual images of an object, when the object is at $u_{1}$ and $u_{2}$ distances respectively. If the size of the virtual image is double that of the real image, then the focal length of the lens is (take, the magnification of the real image as $m$ )
- Two spheres $P$ and $Q$, each of mass $200\, g$ are attached to a string of length one metre as shown in the figure. The string and the spheres are then whirled in a horizontal circle about $O$ at a constant angular speed. The ratio of the tension in the string between $P$ and $Q$ to that of between $P$ and $O$ is $(P$ is at mid-point of the line joining $O$ and $Q$ )
- The volume of $0.02\, M$ acidified permanganate solution required for complete reaction of $60\, mL$ of $0.01\, MI^{-}$ ion solution to form $I_2$ in $mL$ is
View More Questions