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

$A$ flat horizontal board moves up and down in $S.H.M.$ vertically with amplitude $A$. The shortest permissible time period of the vibration such that an object placed on the board may not lose contact with the board is ..........

$A$ body of mass $m$ is suspended to an ideal spring of force constant $k$. The expected change in the position of the body due to an additional force $F$ acting vertically downwards is

Two particles $A$ and $B$ of equal masses are suspended from two massless springs of spring constants $K_{1}$ and $K_{2}$ respectively. If the maximum velocities during oscillations are equal,the ratio of the amplitude of $A$ and $B$ is

$A$ particle of mass $m$ is attached to $3$ springs $A$,$B$ and $C$ of equal force constant $K$ as shown in the figure. If the particle is pushed slightly along the line of spring $C$ and released,find the period of oscillation.

$A$ mass on a spring oscillates up and down. As the mass moves downward from its highest point to its equilibrium point:

Vedclass Test Series

Exam Paper Generator

Online Exam Module