A particle moving in the $xy$-plane experiences a velocity dependent force $F = k\left( {{v_y}\hat i + {v_x}\hat j} \right),$ where ${v_x}{\rm{ }}$ and ${v_y}$ 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?

F arises due to a magnetic field.

Kinetic energy of particle is constant in time.

Quantity $v \cdot a$ is constant in time.

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NEET UG PHYSICS MCQ: MAGNETIC EFFECT OF CURRENT

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A particle moving in the

xy

-plane experiences a velocity dependent force

F = k\left( {{v_y}\hat i + {v_x}\hat j} \right),

where

{v_x}\mathrm{ }

and

{v_y}

are the

x

and

y

components of its velocity

v.

a

is the acceleration of the particle, then which of the following statements is true for the particle?

View answer and explanation

Correct option: A

Quantity

v \times a

is constant in time.

Option C (The proton trajectory will be less curved than the electron trajectory) is correct because the radius of curvature in an electric field is proportional to mass and inversely proportional to charge and electric field strength. Since the proton is much more massive, its trajectory will be less curved.