## Question

A spring which obey’s Hooke’s law extends by 1 cm when a mass is hung on it. It extends by a further 3 cm when the attached mass is moved in a horizontal circle making 2 revolutions per second. What is the length of the unstretched spring? Take

### Solution

21 cm

According to Hookes’ law, the stretching force *F* = *kx*, where *k* is the force constant and *x*, the extension of the spring. A force *mg* stretches the spring by 1 cm. When the mass is describing the horizontal circle, total stretching = 1 + 3 = 4 cm. Hence

Referring to fig, the horizontal component *T* sin θ provides the necessary centripetal force for circular motion, i.e.

. Let *L* cm be the length of the unstretched spring. Then *AC* = (*L* + 4) cm and *r* = (*L* + 4) sin θ.

or *L* = 25 – 4 = 21 cm.

#### SIMILAR QUESTIONS

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