A particle moving in the xy plane experiences a velocity dependent force F→=kvyi^+vxj^, where vx and vy are the x and y components of its velocity v→. If a→ is the acceleration of the particle, then which of the following statements is true for the particle?

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Kinetic energy of particle is constant in time

Quantity v→. a→ is constant in time

Quantity v→ × a→ is constant in time

F→ arises due to a magnetic field

answer is C.

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Detailed Solution

let mass of the particle is m then a→=km vyi^+vxj^ and v→=vxi^+vyj^Let km=α (constant) So αvy=dvxdt and αvx=dvydtDividing, dvxdvy=vyvx⇒∫vxdvx=∫vydvy⇒vx2−vy2=constantNow, v→×a→=vxi^+vyj^×kmvyi^+vxj^=kmvx2−vy2k^ = constant

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