## Question

A small trolley of mass 2 kg resting on a horizontal frictionless turntable is connected by a light spring to the centre of the table. The relaxed length of the spring is 35 cm. When the turntable is rotated an angular frequency of 10 rad s^{–1}, the length of the spring becomes 40 cm. what is the force constant of the spring? ^{ }

### Solution

The radius of the circle along which the trolley moves is

*r* = 40 cm = 0.4 m

When the table is rotated, the tension in the spring is equal to the centripetal force, i.e.

The extension in the spring is *x* = 40 – 35 = 5 cm = 0.05 m

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