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One end of a massless spring of spring c...

One end of a massless spring of spring constant 100 N/m and natural length 0.5 m is fixed and the other end is connected to a particle of mass 0.5 kg lying on as frictionless horizontal table. The spring remains horizontal. If the mass is made to rotate at an angular velocity of 2 rad/s, find the elongation of the spring.

Text Solution

Verified by Experts

The restoring force in the spring provides the centripetal force to the mass.
If .x. is the extension in the spring, then
`Kx=m(L+x)omega^(2)`
Putting the values,
we get
`x=(0.5xx4xx0.5)/(100-0.5xx4)`
`x ~~ 1 cm`
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