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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 anytime $t$ 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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θ=00

θ=300

θ=900

θ=1800

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detailed solution

Correct option is C

2.cosi^+2sintj^ F→=dP→dt=−2sint^+2cotj^ ⇒F→.P→=F.Pcosθ ⇒cosθ=F→.P→FP=−4sintcost+4sint.costF.P.=0 ⇒θ=900

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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 anytime t is Px=2cost,Py=2sint . The angle θ between F→ and P→ at a given time t will be :

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Ready to Test Your Skills?

free study material

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 anytime $t$ 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 :