A particle moves in x − y plane under the influence of a force F such that its linear momentum is p ( t ) = i ^ cos ( kt ) − j ^ sin ( kt ) . If k is constant, the angle between F and p will be

Question

A particle moves in x − y plane under the influence of a force F such that its linear momentum is p ​ ( t ) = i ^ cos ( kt ) − j ^ ​ sin ( kt ) . If k is constant, the angle between F and p ​ will be :

TestHub · Accepted Answer

​ P = cos ( kt ) i ^ − sin ( kt ) j ^ ​ ; ∣ P ∣ = 1 ∵ P = m v ∴ P ^ = v ^ ⇒ v ^ = cos ( kt ) i ^ − sin ( kt ) j ^ ​ a ^ = k − k sin ( kt ) i ^ − k cos ( kt ) j ^ ​ ​ ⇒ a ^ = − sin k t i ^ − cos kt j ^ ​ ∵ F ^ = a ^ = − sin kt i ^ − cos kt j ^ ​ cos θ = ∣ F ^ ∣∣ P ^ ∣ F ^ ⋅ P ^ ​ = − 1 × 1 sin kt cos t + sin kt cos t ​ = 0 ⇒ θ = 2 π ​ ​

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