A particle moving in the xy plane experiences a velocity dependent force F-kvy-vx- where vx and vy are 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-

Given, F=k(v_yî+v_xĵ) ∴ F_x=kv_yî, F_y=kv_xĵ mdv_xdt=kv_y⇒dv_xdt=kmv_y Similarly, nbsp;dv_y dt=kmv_x dv_ydv_x=v_xv_y⇒∫ v_ydv_y=∫ v_xdv_x v_y^2=v_x^2+C v_ ...

265

You visited us 265 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard XII

Physics

Vector Components

A particle mo...

Question

A particle moving in the $x y$ plane experiences a velocity dependent force $\to F = k (v_{y}^i + v_{x}^j),$ where $v_{x}$ and $v_{y}$ are $x$ and $y$ components of its velocity $\to v .$ If $\to a$ is the acceleration of the particle, then which of the following statements is true for the particle?

Quantity

\to v \times \to a

is constant in time

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

\to F

arises due to a magnetic field

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Kinetic energy of particle is constant in time

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Quantity

\to v . \to a

is constant in time

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is A Quantity $\to v \times \to a$ is constant in time
Given, $\to F = k (v_{y}^i + v_{x}^j)$

$∴ F_{x} = k v_{y}^i, F_{y} = k v_{x}^j$

$\frac{m d v_{x}}{d t} = k v_{y} \Rightarrow \frac{d v_{x}}{d t} = \frac{k}{m} v_{y}$

Similarly, $\frac{d v_{y}}{d t} = \frac{k}{m} v_{x}$

$\frac{d v_{y}}{d v_{x}} = \frac{v_{x}}{v_{y}} \Rightarrow \int v_{y} d v_{y} = \int v_{x} d v_{x}$

$v_{y}^{2} = v_{x}^{2} + C$

$v_{y}^{2} - v_{x}^{2} = constant$

$\to v \times \to a = (v_{x}^i + v_{y}^j) \times \frac{k}{m} (v_{y}^i + v_{x}^j)$

$= (v_{x}^{2}^k - v_{y}^{2}^k) \frac{k}{m} = (v_{x}^{2} - v_{y}^{2}) \frac{k}{m}^k = constant$

Hence, option $(A)$ is correct.

Suggest Corrections

Similar questions

Q. The velocity components of a particle moving in the xy plane of the reference frame

K

are equal to

v_{x}

and

v_{y}

. Find the velocity

v^{'}

of this particle in the frame

K^{'}

which moves with the velocity

V

relative to the frame

K

in the positive direction of its x axis.

Q. A particle is moving in the x-y plane. At certain instant of time,the components of its velocity and acceleration are as follows:

v_{x} = 3 m s^{- 1}

v_{y} = 4 m s^{- 1}

a_{x} = 2 m s^{- 2}

and

a_{y} = 1 m s^{- 1}

. The rate of change of speed at this moment is:

Q. A particle is moving in the

x - y

plane. At certain instant of time, the components of its velocity and acceleration are as follows:

v_{x} = 3 {ms}^{- 1}, v_{y} = 4 {ms}^{- 1}, a_{x} = 2 {ms}^{- 2}

and

a_{y} = 1 {ms}^{- 2}

. The rate of change of speed at this moment is

Q. A particle moves in the x-y plane with velocity

v_{x} = 8 t - 2

and

v_{y} = 2

. If it passes through the point x=14 and y=4 at t=2s, then the equation of the path is:

Q. A particle moves in the x-y plane with velocity

v_{x} = 8 t - 2

and

v_{y} = 2.

If it passes through the point x= 14 and y= 4 at t= 2s, the equation of the is:

Join BYJU'S Learning Program

A particle moving in the xy plane experiences a velocity dependent force →F=k(vy^i+vx^j), where vx and vy are 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?