Question 158: Centre of Mass and Rotational Motion

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 :

Accepted Answer

$m{\omega ^2}({l_0} + x) = kx$
$ \Rightarrow m{\omega ^2}{l_0} = (k - m{\omega ^2}) 	imes x$
$ \Rightarrow x = {{m{\omega ^2}{l_0}} \over {(k - m{\omega ^2})}}$

Answer

${{k - m{\omega ^2}{l_0}} \over {m{\omega ^2}}}$

Answer

${{m{\omega ^2}{l_0}} \over {k + m{\omega ^2}}}$

Answer

${{m{\omega ^2}{l_0}} \over {k - m{\omega ^2}}}$

Answer

${{k + m{\omega ^2}{l_0}} \over {m{\omega ^2}}}$

Centre of Mass and Rotational Motion

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