The total mechanical enegry of a particle is `E`. The speed of the particle at `x = ((2E)/(K))^(1//2)` is `((2E)/(m))^(1//2)`. Find the potential energy of the particle at `x` :

Options

A. zero
B. `(1)/(2) Kx^(2)`
C. `(1)/(4) Kx^(2)`
D. `(2)/(5) Kx^(2)`

Answer

A

Explanation

At `x = ((2E)/(K))^(1//2), v =((2E)/(m))^(1//2)`
or `v^(2) =(2E)/(m)` or `(1)/(2) mv^(2) = E`
So, at `x= ((2E)/(K))^(1//2)`, kinetic energy is equal to total mechanical energy.
Hence, `PE` at `x = ((2E)/(K))^(1//2)` is zero.
So, `U (x) = 0`.