Question:
A body of mass $100\text{ gram}$ is tied to a spring of spring constant $8\text{ N/m}$, while the other end of a spring is fixed. If the body moves in a circular path on smooth horizontal surface with constant angular speed $8\text{rad/s}$ then the ratio of extension in the spring to its natured length will be}
A body of mass $100\text{ gram}$ is tied to a spring of spring constant $8\text{ N/m}$, while the other end of a spring is fixed. If the body moves in a circular path on smooth horizontal surface with constant angular speed $8\text{rad/s}$ then the ratio of extension in the spring to its natured length will be}
Show Hint
For spring-based circular motion, do not forget that radius becomes:
\[
r=l+x
\]
not just the extension \(x\).
Updated On: May 14, 2026
- $1 : 1$
- $8 : 1$
- $2 : 1$
- $4 : 1$
Show Solution
Verified By Collegedunia
The Correct Option is D
Solution and Explanation
Concept:
The spring force provides centripetal force. If natural length is \(l\) and extension is \(x\), then radius of circular path is: \[ r=l+x \] Also, \[ kx = m\omega^2 r \] ip
Step 1: Write the given values.
\[ m=100\text{ g}=0.1\text{ kg} \] \[ k=8\text{ N/m} \] \[ \omega=8\text{ rad/s} \] ip
Step 2: Apply centripetal force condition.
\[ kx = m\omega^2(l+x) \] Substitute values: \[ 8x = 0.1\times 64 (l+x) \] \[ 8x = 6.4(l+x) \] \[ 8x = 6.4l + 6.4x \] \[ 1.6x = 6.4l \] \[ x=4l \] ip
Step 3: Find the ratio of extension to natural length.
\[ x:l = 4:1 \] ip Hence, the correct answer is:
\[ \boxed{(D)\ 4:1} \]
The spring force provides centripetal force. If natural length is \(l\) and extension is \(x\), then radius of circular path is: \[ r=l+x \] Also, \[ kx = m\omega^2 r \] ip
Step 1: Write the given values.
\[ m=100\text{ g}=0.1\text{ kg} \] \[ k=8\text{ N/m} \] \[ \omega=8\text{ rad/s} \] ip
Step 2: Apply centripetal force condition.
\[ kx = m\omega^2(l+x) \] Substitute values: \[ 8x = 0.1\times 64 (l+x) \] \[ 8x = 6.4(l+x) \] \[ 8x = 6.4l + 6.4x \] \[ 1.6x = 6.4l \] \[ x=4l \] ip
Step 3: Find the ratio of extension to natural length.
\[ x:l = 4:1 \] ip Hence, the correct answer is:
\[ \boxed{(D)\ 4:1} \]
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 Springs Questions
- Three springs having spring constants \( k \), \( 2k \), and \( 3k \) are connected (i) in series and (ii) in parallel. Let the effective spring constants for the series and parallel combinations be \( k_s \) and \( k_p \) respectively. What is the ratio \( \frac{k_p}{k_s} \)?
- If the period of a oscillation of mass ' m ' suspended from a spring is $2\text{ s}$ , then the period of suspended mass ' 4 m ' with the same spring will be}
- A vertical spring oscillates with period 6 second with mass $m$ is suspended from it. When the mass is at rest, the spring is stretched through a distance of (Take, $g = \pi^2 = 10 \text{ m/s}^2$ )
- A vertical spring oscillates with period 6 second with mass $m$ is suspended from it. When the mass is at rest, the spring is stretched through a distance of (Take, $g = \pi^2 = 10 \text{ m/s}^2$ )
- A sphere of mass 25 gram is placed on a vertical spring. It is compressed by 0.2 m using a force 5 N. When the spring is released, the sphere will reach a height of \( g = 10 \, \text{m/s}^2 \)
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