A force `F= -khati+xhatj` where k is a positive constant, acts on a praricle moving in the xy plane. Starting from the origin, the particle is taken along the positive x - axis to the point (a,0) and then parallel to the y-axis to the point (a,a) the total work done by the formce on the particle is

Options

A. `-2 K a^2`
B. `2 Ka^2`
C. `-Ka^2`
D. `Ka^2`

Answer

C

Explanation

`w = int f_x dx + int f_y dy = -k int ydx - k int xdy`
From 0 to A, `dy = 0, y = 0`
So, `W_(QA) = 0`
From A to B : `dx = 0, x = a, W_(AB) = -ka int_(0)^a dy = -ka^2`
Hence, total work done `W_T = W_(OA) + W_(AB) = 0 - ka^2 = -ka^2`