Question

A particle of mass m is moving in the space under the influence of a force $\overline{F}=\overline{V}\times \overline{A}$ where $\overline{V}$ is the velocity of particle and A is constant vector given as $A=A\hat{k}$ . At t = 0, particle is at origin and moving with initial ${\underset{V}{\to }}_0=v_1\hat{i}+v_2\hat{k}$. Choose the CORRECT statement(s).

• A. The magnitude of linear momentum of the particle is constant
• B. Velocity of particle at any time t is $v_1\cos \left(\frac{A}{m}t\right)\hat{i}-v_1\sin \left(\frac{A}{m}t\right)\hat{j}+v_2\hat{k}$
• C. Particle will perform motion on helical path with constant pitch
• D. Magnitude of angular velocity of the particle is variable

Answer 1

Answer: (A), (B), (C)

The correct options are
A The magnitude of linear momentum of the particle is constant
B Velocity of particle at any time t is $v_1\cos \left(\frac{A}{m}t\right)\hat{i}-v_1\sin \left(\frac{A}{m}t\right)\hat{j}+v_2\hat{k}$
C Particle will perform motion on helical path with constant pitch

$\overrightarrow{F}=(v_1\hat{i}+v_2\hat{k})\times \left(A\hat{k}\right)=Av(-\hat{j})$

$\frac{m{v}^2}{R}=Av\Rightarrow R=\frac{mv}{A}\Rightarrow \omega =\frac{A}{m}$

$\overrightarrow{v}=v_1\cos \theta \hat{i}-v_1\sin \theta \hat{j}+v_2\hat{k}$

$\overrightarrow{v}=v_1\cos \left(\frac{A}{m}t\right)\hat{i}-v_1\sin \left(\frac{A}{m}t\right)\hat{j}+v_2\hat{k}$