A body is executing simple harmonic motion. At a displacement x its potential energy is `E_1` and at a displacement y its potential energy is `E_2`. The potential energy (E) at a discplcement (x+y) is,

Options

A. `sqrt(E)=sqrt(E_1)-sqrt(E_2)`
B. `sqrt(E)=sqrt(E_1)+sqrt(E_2)`
C. `E=E_1+E_2`
D. `E=E_1-E_2`

Answer

b

Explanation

The potential energy,
`E=1/2Kx^2`
`E_1=1/2Kx^2`
`sqrt(E_1)=sqrt(K/2x`
`E_1=1/2Ky^2`…..(i)
`sqrtE=sqrt(K)/(2)(X+Y)`…(ii)
At displacement `(x+y)=1/2(x+y)^2`
`sqrtE=sqrt(K)/(2)(X+Y)`
From equation (1),(2) and(3),
`sqrt(k)/(2)(x+y)=sqrt(k)/(2)x+sqrt(k)/(2)y`
`sqrtE=sqrtE_1+sqrt(E_2)`