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Q.

An undeformed spring with spring constant $k$ has length $l_{0}$ . When the system rotates at an angular velocity $ω$ , the weight with mass m causes an extension in the spring. If $l$ is the length of the rotating spring then

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a

$l = \frac{m l_{0} ω^{2}}{k}$

b

$l = l_{0} + \frac{m l_{0} ω^{2}}{k}$

c

$l = \frac{k l_{0}}{k - m ω^{2}}$

d

$l = l_{0} - \frac{m l_{0} ω^{2}}{k}$

answer is C.

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Detailed Solution

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Restoring Force = Centripetal Force

$k (l - l_{0}) = m l ω^{2}; l (k - m ω^{2}) = k l_{0}; l = \frac{{kl}_{0}}{k - m ω^{2}}$

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An undeformed spring with spring constant k has length l0 . When the system rotates at an angular velocity ω , the weight with mass m causes an extension in the spring. If l is the length of the rotating spring then