A particle moves in the x - y plane under the action of a force F such that the coordinates of its linear momentum P → at any time t is p x = 2 cos t , p y = 2 sin ⁡ t The angel θ between F → and P → at a given time t will be

Step-by-step solution

P = p x 2 + p y 2 = 2 cos ⁡ t 2 + 2 sin ⁡ t 2 = 2 If m be the mass of the body, then kinetic energy = p 2 2 m = 2 2 2 m = 2 m Since kinetic energy does not change with time, both work done and power are zero Now Power = F v cos ⁡ θ = 0 As F ≠ 0 , v ≠ 0 ∴ cos ⁡ θ = 0 Or θ = 90 ° As direction of p → is same that v → ( ∵ p → = m v → ) hence angle between F → and p → is equal to 90 °