Question

The force acting on a particle in one dimension is F = ax - 2xβ³. The corresponding potential energy V(x), assuming V(0) = 0 is given by ______.

विकल्प

• V(x) = `alphax^2 - 2 beta x^4`

• V(x) = `1/2 alpha x^2 + 1/2 beta x^4`

• V(x) = `alphax^2 + 2 beta x^4`

• V(x) = `-1/2 alphax^2 - 1/2 beta x^4`

Answer 1

The force acting on a particle in one dimension is F = ax - 2xβ³. The corresponding potential energy V(x), assuming V(0) = 0 is given by `underline("V"(x) = 1/2 alpha x^2 + 1/2 beta x^4`.

Explanation:

`int_0^"v" "dv" = - int_0^"v" bar"F" * "dx"`

v = `- int_0^"v" (- alphax - 2betax^3)"dx" = (alphax^2)/2 + (betax^4)/2`