A particle is acted by `x` force `F = Kx` where `K` is `a( + ve)` constant its potential energy at `x = 0` is zero . Which curve correctly represent the variation of potential energy of the block with respect to `x`

Options

A.
B.
C.
D.

Answer

B

Explanation

We know that `Delta U = -W` for conservation forces
`:. Delta U = - int_(0)^x Fdx = - int_0^x K xdx implies U_(x) - U_(0) = -(kx^2)/(2)`
Given `U_(0) = 0`. Therefore, `U_(x) = -(kx^2)/(2)` .