A particle moves in the $$x-y$$ plane under the action of a force F→ such that the value of its linear momentum P→ at any time t is Px $$=$$ $$2$$ $$cos$$ t, Py $$=$$ $$2$$ $$sin$$ t. The angle θ between F→ and P→ at a given time t will be

Question

A particle moves in the $$x-y$$ plane under the action of a force F→ such that the value of its linear momentum P→ at any time t is Px $$=$$ $$2$$ $$cos$$ t, Py $$=$$ $$2$$ $$sin$$ t. The angle θ between F→ and P→ at a given time t will be

Infinity Learn · Accepted Answer

P $$=$$ $$Px2+Py2$$ $$=$$ (2$$ $$cos$$ $$t)2+(2$$ $$sin$$ $$t)2$$ $$=$$ $$2If$$ m be the mass of the body, thenKinetic energy $$=$$ $$P22m$$ $$=$$ $$(2)22m$$ $$=$$ $$2$$ mSince kinetic energy does not change with time, both work done and power are zero.Now Power $$=$$ Fv $$cos$$ θ $$=$$ $$0As$$  F ≠$$0$$, v ≠$$0$$            ∴$$cos$$ θ or θ $$=$$ $$900As$$ direction of P→ is same that v→ $$($$∴ P→ $$=$$ mv→$$), hence angle between F→ and P→ is equal to $$900$$

A particle moves in the x-y plane under the action of a force $\vec{F}$ such that the value of its linear momentum $\vec{P} at any time t is P_{x} = 2 \cos t,$
$P_{y} = 2 \sin t$ . The angle $θ$ between $\vec{F}$ and $\vec{P}$ at a given time t will be

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

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A particle moves in the x-y plane under the action of a force $\vec{F}$ such that the value of its linear momentum $\vec{P} at any time t is P_{x} = 2 \cos t,$
$P_{y} = 2 \sin t$ . The angle $θ$ between $\vec{F}$ and $\vec{P}$ at a given time t will be