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 trough fixed end, then the elongation of the spring will be

Step-by-step solution

The particle is moving in a horizontal circle, so it is accelerated towards the centre with magnitude v 2 r . The horizontal force on the particle is due to the spring and is given by k x , where x is the elongation and k is the spring constant. k x = m v 2 r = m ω 2 r = m ω 2 l 0 + x ⇒ k - m ω 2 x = m ω 2 l 0 ⇒ x = m ω 2 l 0 k - m ω 2