Question:
Two rods of the same material and volume having circular cross-section are subjected to tension \( T \). Within the elastic limit, the same force is applied to both the rods. Diameter of the first rod is half of the second rod, then the extensions of the first rod to second rod will be in the ratio
Two rods of the same material and volume having circular cross-section are subjected to tension \( T \). Within the elastic limit, the same force is applied to both the rods. Diameter of the first rod is half of the second rod, then the extensions of the first rod to second rod will be in the ratio
Show Hint
Remember, the extension in a rod is inversely proportional to its cross-sectional area.
Updated On: Jan 27, 2026
- 4:1
- 16:1
- 32:1
- 2:1
Show Solution
Verified By Collegedunia
The Correct Option is A
Solution and Explanation
Step 1: Relation for extension.
The extension \( \Delta L \) in a rod under tension is given by: \[ \Delta L = \frac{F L}{A Y} \] where \( F \) is the applied force, \( L \) is the length of the rod, \( A \) is the cross-sectional area, and \( Y \) is Young's modulus.
Step 2: Area and length relation.
Since the diameters of the rods are in the ratio 1:2, the areas \( A_1 \) and \( A_2 \) are in the ratio \( (1:2)^2 = 1:4 \). Thus, the extensions are in the inverse ratio of the areas, i.e., 4:1.
Step 3: Conclusion.
Thus, the correct answer is (A) 4:1.
The extension \( \Delta L \) in a rod under tension is given by: \[ \Delta L = \frac{F L}{A Y} \] where \( F \) is the applied force, \( L \) is the length of the rod, \( A \) is the cross-sectional area, and \( Y \) is Young's modulus.
Step 2: Area and length relation.
Since the diameters of the rods are in the ratio 1:2, the areas \( A_1 \) and \( A_2 \) are in the ratio \( (1:2)^2 = 1:4 \). Thus, the extensions are in the inverse ratio of the areas, i.e., 4:1.
Step 3: Conclusion.
Thus, the correct answer is (A) 4:1.
Was this answer helpful?
0
0
Top MHT CET Physics Questions
- In non uniform circular motion, the ratio of tangential to radial acceleration is (r = radius of circle, $v =$ speed of the particle, $\alpha =$ angular acceleration)
- A particle moves along a circle of radius ?$r$? with constant tangential acceleration. If the velocity of the particle is ?$?$? at the end of second revolution, after the revolution has started then the tangential acceleration is
- If $M_z$ = magnetization of a paramagnetic sample, $B$ = external magnetic field, $T$ = absolute temperature, $C$ = curie constant then according to Curie�s law in magnetism, the correct relation is
- In a fundamental mode, the time required for the sound wave to reach upto the closed end of a pipe filled with air is $'t'$ second. The frequency of vibration of air column is
- In a parallel plate capacitor, the capacity increases if
View More Questions
Top MHT CET Waves and Oscillations Questions
- For a particle performing linear S.H.M., its average speed over one oscillation is (a = amplitude of S.H.M., n = frequency of oscillation)
- The displacement of a particle performing simple harmonic motion is given by, x=8sin$\omega t+6cos \omega t$, where distance is in cm and time is in second. The amplitude of motion is
- The minimum phase difference between two simple harmonic oscillations, $ \, \, \, \, \, \, \, \, y_1 =\frac{1}{2}sin \omega t +\frac{\sqrt 3}{2} cos \omega t$ $ \, \, \, \, \, \, \, \, \, \, \, y_2 =sin \omega t +cos \omega t$ is
- For a particle in $ SHM $ , if the amplitude of the displacement is a and the amplitude of velocity is $ v $ , the amplitude of acceleration is
- The average acceleration of a particle performing $ SHM $ over one complete oscillation is
View More Questions
Top MHT CET Questions
- During r- DNA technology, which one of the following enzymes is used for cleaving DNA molecule ?
- In non uniform circular motion, the ratio of tangential to radial acceleration is (r = radius of circle, $v =$ speed of the particle, $\alpha =$ angular acceleration)
- The temperature of $32^{\circ}C$ is equivalent to
- The line $5x + y - 1 = 0$ coincides with one of the lines given by $5x^2 + xy - kx - 2y + 2 = 0 $ then the value of k is
- The heat of formation of water is $ 260\, kJ $ . How much $ H_2O $ is decomposed by $ 130\, kJ $ of heat ?
View More Questions