Kinematics

JEE Main level, single correct, medium

37 of 308

Question 37 of 308

A particle moving in the xyxy-plane experiences a velocity dependent force F⃗=k(υyi^+υxj^)\vec{F}=k\left({υ}_{y}\hat{i}+{υ}_{x}\hat{j}\right), where υx{υ}_{x} and υy{υ}_{y} are the xx and yy components of its velocity υ⃗\vec{υ}. If a⃗\vec{a} is the acceleration of the particle, then which of the following statements is true for the particle ?

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Answer: (A) quantity υ⃗×a⃗\vec{υ}\times \vec{a} is constant in time

F⃗=kv⃗\vec{F}=k\vec{v}
⇒\Rightarrow F⃗‖v⃗\vec{F}‖\vec{v}
⇒\Rightarrow a⃗‖v⃗\vec{a}‖\vec{v}
⇒\Rightarrow v⃗×a⃗=0\vec{v}\times \vec{a}=0 always

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