Question

A body is executing simple harmonic motion As `x` displacement `x` its potential energy is `E_(1)` and at a displacement `y` its potential energy is `E_(2)` The potential energy `E` at displacement `(x+y)` is
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 1

Correct Answer - B
`E_(1) = (1)/(2) Kx^(2) rArr x = sqrt((2E_(1))/(K)`
`E_(2) = (1)/(2) Ky^(2) rArr y = sqrt((2E_(2))/(K)`
` and E = (1)/(2) K(x+y)^(2) rArr x + y = sqrt((2E)/(K)`
`rArr sqrt((2E_(1))/(K)) + sqrt((2E_(2))/(K)) = sqrt((2E)/(K)) rArr sqrt(E_(1))+sqrt(E_(2)) = sqrt(E)`