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Q.

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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a

Kinetic energy of particle is constant in time

b

Quantity v→. a→  is constant in time

c

Quantity  v→ ×  a→  is constant in time

d

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=constant​​Now, v→×a→=vxi^+vyj^×kmvyi^+vxj^=kmvx2−vy2k^ = constant
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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?