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 coordinates `(3, 3)`, only under the action of potential field force. Then its kinetic energy T at the instant when the particle is at a point with the coordinates `(1,1)` is

Options

A. `8 alpha`
B. `24 alpha`
C. `16 alpha`
D. zero

Answer

C

Explanation

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