A spring which is initially in un-streatched condition, is first stretched by a length x and again by a further length x. The work done in the first case W_(1) is one third of the work done in second case W_(2). True of false ?

A spring which is initially in un-streatched condition, is first stret

1.	A spring which is initially in un-streatched condition, is first stretched by a length x and again by a further length x. The work done in the first case W_(1) is one third of the work done in second case W_(2). True of false ?
Answer» Solution :The AMOUNT of work done to stretching distance X `W_(1)=1/2k^(2) thereforek=(2W_(1))/x^(2)` Total work done in stretchig the spring through a distance `2x "is" W_(2)=1/2k(2x)^(2)` `W_(2)1/2((2W_(1))/ x^(2))4x^(2)=4W_(1)` Extra work REQUIRED to stretch the additional x distance is `W=W_(2)-W_(1)=4W_(1)-W_(1)=3W^(1)` `THEREFORE W_(1)=1/3W` Hence it is true.