A particle is exeuting `SHM`. At a point `x = A//3`, kinetic energy of the particle of the particle is `K`, where A is the particle At a point `x = 2A//3`, kinetic energy of the particle will be:

Options

A. `2K`
B. `Ksqrt(2)`
C. `(5)/(8)K`
D. `(5)/(3) K`

Answer

C

Explanation

`v = omega sqrt((A^(2) -x^(2))) rArr v prop sqrt((A^(2) -x^(2)))`
At `x = A//3`
`sqrt((A^(2) - x^(2))) = sqrt((A^(2) - (4A^(2))/(9))) = A sqrt((8)/(9))`
At `x = 2A//3`
sqrt((A^(2) - x^(2))) = sqrt((A^(2) - (4A^(2))/(9))) = A sqrt((5)/(9))`
`K' = (5)/(8) xx (9)/(8) K = (5)/(8) K`