BITSAT 2015 Paper

In the string elastic force is conservative in nature.
∴ W = - ΔU
Work done by elastic force of string,
W = - (UF−Ui) = Ui−UF
W =

1

2

kx2−

k

2

(x+y)2
=

1

2

kx2−

1

2

k(x2+y2+2xy)
=

1

2

kx2−

1

2

ky2 -

1

2

kx2−

1

2

k(2xy)
= - kxy -

1

2

ky2
Therefore, the work done against elastic force
Wexternal = - W = 1/2 Ky(2x + y)