Question

A particle moves in the XY Plane under the action of a force F such that the components of its linear momentum P at any time t are Px = 2 cost, Py = 2sint. The angle between F and P at time t is 

(A) 90° 

(B) 0° 

(C) 180° 

(D) 30°

Answer 1

Correct option: (A) 90°

Explanation:

P = P_x i˄ + P_yj˄

P = 2 cos t i˄ + 2 sin t j˄

F = (d / dt) (p) = (d / dt) (2 cos t i˄ + 2 sin t j˄)

F = – 2 sin t i˄ + 2 cos t j˄

cos θ = {(F∙P) / (|F||P|)}

F ∙ P = (– 2 sin t i˄ + 2 cos t j˄)(2 cos t i˄ + 2 sin t j˄)

= – 4 sin t cos t + 4 sin t cos t

= 0

cos θ = 0

θ = 90°