Question

If the total energy of a particle executing SHM is E, then the potential energy V and the kinetic energy K of the particle in terms of E when its displacement is half of its amplitude will be ______.

विकल्प

• V = `"E"/4` and K = `(3"E")/4`

• V = `"3E"/4` and K = `"E"/4`

• V = `(3"E")/4` and K = `"E"/4`

• V = `"E"/4` and K = `"E"/4`

Answer 1

V = `"E"/4` and K = `(3"E")/4`

Explanation:

E = k + v and k = `1/2 "mw"^2 ("A"^2 + "y"^2)`

and E = `1/2`mw²A² 

∴ y = `"A"/2`

∴ k = `1/2 "mw"^2 ["A"^2 - ("A2"/2)^2]`

`= 1/2 "mw"^2 "A"^2 (3/4) = (3"E")/4`

∴ V = E - K = E - `3/4"E" = "E"/4`