A spring-mass system (mass m,spring constant | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(D) Let $\Delta \ell$ be the extension in the spring due to the rotation of the disc.The total length of the spring becomes $r = \ell_{0} + \Delta \el

Vedclass · Accepted Answer

$\frac{m \omega^{2}}{k}$

Vedclass · Answer

(D) Let $\Delta \ell$ be the extension in the spring due to the rotation of the disc.The total length of the spring becomes $r = \ell_{0} + \Delta \ell$.The centripetal force required for the circular motion of the mass $m$ is provided by the spring force.Thus,$k \Delta \ell = m \omega^{2} r = m \omega^{2} (\ell_{0} + \Delta \ell)$.Rearranging the equation: $k \Delta \ell - m \omega^{2} \Delta \ell = m \omega^{2} \ell_{0}$.$\Delta \ell (k - m \omega^{2}) = m \omega^{2} \ell_{0}$.$\Delta \ell = \frac{m \omega^{2} \ell_{0}}{k - m \omega^{2}}$.Since it is given that $k >> m \omega^{2}$,we can approximate $k - m \omega^{2} \approx k$.Therefore,$\Delta \ell \approx \frac{m \omega^{2} \ell_{0}}{k}$.The relative change in length is $\frac{\Delta \ell}{\ell_{0}} = \frac{m \omega^{2}}{k}$.

Similar Questions

$A$ spring has a certain mass suspended from it and its period for vertical oscillations is $T_1$. The spring is now cut into two equal halves and the same mass is suspended from one of the halves. The period of vertical oscillations is now $T_2$. The ratio $T_1 / T_2$ is

The potential energy of a particle of mass $0.1\,kg,$ moving along the $x-$axis,is given by $U = 5x(x-4)\,J,$ where $x$ is in metres. It can be concluded that

$A$ silver atom in a solid oscillates in simple harmonic motion in a specific direction with a frequency of $10^{12} \ s^{-1}$. What is the force constant of the bonds connecting one atom to the others? (Molar mass of silver $= 108 \ g/mol$ and Avogadro number $= 6.02 \times 10^{23} \ mol^{-1}$)

For the system given below,find the angular frequency of oscillation.

Two bodies $M$ and $N$ of equal masses are suspended from two separate massless springs of force constants $k_1$ and $k_2$ respectively. If the two bodies oscillate vertically such that their maximum velocities are equal,the ratio of the amplitude of $M$ to that of $N$ is

Vedclass Test Series

Exam Paper Generator

Online Exam Module