Question:
Two wires of lengths l and 2l, radii r and 2r respectively having same Young's modulus are hung with a weight mg. Net elongation is
Two wires of lengths l and 2l, radii r and 2r respectively having same Young's modulus are hung with a weight mg. Net elongation is
Show Hint
Two wires of lengths l and 2l, radii r and 2r respectively having same Young's modulus are hung with a weight mg. Net elongation is
Updated On: Apr 15, 2026
- $\frac{3mgl}{\pi r^{2}Y}$
- $\frac{2mgl}{3\pi r^{2}Y}$
- $\frac{3mgl}{2\pi r^{2}Y}$
- $\frac{3mgl}{4\pi r^{2}Y}$
Show Solution
Verified By Collegedunia
The Correct Option is C
Solution and Explanation
Step 1: Formula
Elongation $\Delta l = \frac{Fl}{AY} = \frac{mgl}{\pi r^2 Y}$.
Step 2: Individual Elongations
Wire 1: $l_1 = \frac{mgl}{\pi r^2 Y}$. Wire 2: $l_2 = \frac{mg(2l)}{\pi (2r)^2 Y} = \frac{mgl}{2\pi r^2 Y}$.
Step 3: Net Elongation
$L = l_1 + l_2 = \frac{mgl}{\pi r^2 Y} + \frac{mgl}{2\pi r^2 Y} = \frac{3mgl}{2\pi r^2 Y}$.
Final Answer: (C)
Elongation $\Delta l = \frac{Fl}{AY} = \frac{mgl}{\pi r^2 Y}$.
Step 2: Individual Elongations
Wire 1: $l_1 = \frac{mgl}{\pi r^2 Y}$. Wire 2: $l_2 = \frac{mg(2l)}{\pi (2r)^2 Y} = \frac{mgl}{2\pi r^2 Y}$.
Step 3: Net Elongation
$L = l_1 + l_2 = \frac{mgl}{\pi r^2 Y} + \frac{mgl}{2\pi r^2 Y} = \frac{3mgl}{2\pi r^2 Y}$.
Final Answer: (C)
Was this answer helpful?
0
0
Top MET Physics Questions
- A coil of 100 turns and area $2 \times 10^{-2}m^2 $ is pivoted about a vertical diameter in a uniform magnetic field and carries a current of 5A. When the coil is held with its plane in north-south direction, it experiences a couple of 0.33 Nm. When the plane is east-west, the corresponding couple is 0.4 Nm, the value of magnetic induction is [Neglect earth's magnetic field]
- Radiation, with wavelength 6561 $?$ falls on a metal surface to produce photoelectrons. The electrons are made to enter a uniform magnetic field of $3 \times 10^{-4} T$. If the radius of the largest circular path followed by the electrons is 10 mm, the work function of the metal is close to :
- In intrinsic semiconductor at room temperature number of electrons and holes are
- A rope of mass $0.1\, kg$ is connected at the same height of two opposite walls. It is allowed to hang under its own weight. At [he contact point between the rope and the wall, the rope makes an angle $ \theta =10^{\circ} $ with respect to horizontal. The tension in the rope at its midpoint between the walls is
- At great distances from an electric dipole, the electric field strength due to the dipole varies with the distance as
View More Questions
Top MET Questions
- A coil of 100 turns and area $2 \times 10^{-2}m^2 $ is pivoted about a vertical diameter in a uniform magnetic field and carries a current of 5A. When the coil is held with its plane in north-south direction, it experiences a couple of 0.33 Nm. When the plane is east-west, the corresponding couple is 0.4 Nm, the value of magnetic induction is [Neglect earth's magnetic field]
- $\int\limits_{0}^{8}| x -5| d x$ is equal to
- Radiation, with wavelength 6561 $?$ falls on a metal surface to produce photoelectrons. The electrons are made to enter a uniform magnetic field of $3 \times 10^{-4} T$. If the radius of the largest circular path followed by the electrons is 10 mm, the work function of the metal is close to :
- In intrinsic semiconductor at room temperature number of electrons and holes are
- Which of the following product is formed in the reaction $ CH_3MgBr {->[(i)CO_2][(ii)H_2O]} ? $
View More Questions