A particle moving in the xy -plane experiences a velocity dependent force → F = k( υ _ y ^ i + υ _ x ^ j ) , where υ _ x and υ _ y are the x and y components of its velocity → υ . If → a is the acceleration of the

Correct answer: A. quantity → υ × → a is constant in time → F = k → v ⇒ → F ‖ → v ⇒ → a ‖ → v ⇒ → v × → a = 0 always

JEE Main 20206 SeptemberEvening Shift

JEE Main 2020 · 6 September · Evening Shift · Physics · Motion in One Dimension

A particle moving in the xy -plane experiences a velocity dependent...

A particle moving in the

xy

-plane experiences a velocity dependent force

\overset{\to}{F} = k\left({υ}_{y}\overset{^}{i} + {υ}_{x}\overset{^}{j}\right)

, where

{υ}_{x}

and

{υ}_{y}

are the

x

and

y

components of its velocity

\overset{\to}{υ}

. If

\overset{\to}{a}

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

A. quantity $\overset{\to}{υ} \times \overset{\to}{a}$ is constant in time

\overset{\to}{F} = k\overset{\to}{v}

⇒

\overset{\to}{F} ‖ \overset{\to}{v}

⇒

\overset{\to}{a} ‖ \overset{\to}{v}

⇒

\overset{\to}{v} \times \overset{\to}{a} = 0

always