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 

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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 


Correct option is

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.




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