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 $ω$ about an axis passing through fixed end, then the elongation of the spring will be :

• A. $\frac{k-mω^2l_0}{mω^2}$
• B. $\frac{mω^2l_0}{k+mω^2}$
• C. $\frac{mω^2l_0}{k-mω^2}$
• D. $\frac{(k+mω^2l_0)}{mω^2}$

Answer 1

Answer: (C)

$\frac{mω^2l_0}{k-mω^2}$

Answer 2

The elongation of the spring will be :

$mω^2(l_0 \+ x) = kx$

$⇒ mω^2l_0 = (k – mω^2) × x$

$⇒ x=\frac{mω^2l_0}{(k-mω^2)}$