Question

One end of a massless spring of spring constant $k$ and natural length $l_{0}$ is fixed while the other end is connected to a small object of mass $m$ lying on a frictionless table. The spring remains horizontal on the table. If the object is made to rotate at an angular velocity $\omega$ about an axis passing through fixed end, then the elongation of the spring will be:

• A. $\frac{ k - m \omega^{2} l_{0}}{ m \omega^{2}}$
• B. $\frac{ m \omega^{2} l_{0}}{ k + m \omega^{2}}$
• C. $\frac{ m \omega^{2} l_{0}}{ k - m \omega^{2}}$
• D. $\frac{ k + m \omega^{2} l_{0}}{ m \omega^{2}}$

Answer 1

Answer: (C)

$K \Delta x = m \left(\ell_{0}+\underline{\underline{\Delta}} x \right) w ^{2}$
$K \Delta x = m \ell_{0} w ^{2}+ mw ^{2} \Delta x$
$\Delta x =\frac{ m \ell_{0} w ^{2}}{ k - mw ^{2}}$