The potential energy of a particle is determined by the expression `U=alpha(x^(2)+y^(2))`, where `alpha` is a positive constant. The particle begins to move from a point with the co-ordinates (3, 3) only under the action of potential fields force. When it reaches the point
(1, 1) its kinetic energy is `4 Kalpha`. Find the value of K.

Options

A. (a) `8alpha`
B. (b) `24alpha`
C. (c) `16alpha`
D. (d) Zero

Answer

C

Explanation

As the particle moves only under the action of conservative force, its mechanical energy must be conserved. So
`DeltaT+DeltaU=0` (T stands for kinetic energy)
or `DeltaT=-DeltaU=U_i-U_f`
`=alpha(3^2+3^2)-alpha(1^2+1^2)=16alpha`