A particle moving in the xy plane experiences a velocity dependent force F = k(vᵧî + vₓĵ), where vₓ and vᵧ 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?

Option 1 -

quantity v * a is constant in time

Option 2 -

F arises due to a magnetic field.

Option 3 -

kinetic energy of particle is constant in time.

Option 4 -

quantity v · a is constant in time.

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1 Answer

Answered by

alok kumar singh | Contributor-Level 10

a month ago

Correct Option - 1

Detailed Solution:

mdv? /dt = kv? (1) and mdv? /dt = kv?
(2)/ (1) ⇒ dv? /dv? = v? /v?
v? dv? = v? dv?
v? ² = v? ² + C
v? ² – v? ² = C = Constant
Now, v? × a? = (v? î + v? ) × (k/m) (v? î + v? )
= (k/m) [v? ²k? – v? ²k? ] = (k/m) (v? ² – v? ²)k? = Constant.

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