JEE PYQ: Laws Of Motion Question 18
Question 18 - 2020 | 06 Sep Shift 2] (MCQ)
A particle moving in the $xy$ plane experiences a velocity dependent force $\vec{F} = k(v_y\hat{i} + v_x\hat{j})$. If $\vec{a}$ is the acceleration of the particle, then which of the following statements is true?
(1) quantity $\vec{v} \times \vec{a}$ is constant in time [Correct]
(2) $\vec{F}$ arises due to a magnetic field
(3) kinetic energy of particle is constant in time
(4) quantity $\vec{v} \cdot \vec{a}$ is constant in time
Show Answer
Answer: (1)
Solution
$v_x^2 - v_y^2 = C$. $\vec{v} \times \vec{a} = \frac{k}{m}(v_x^2 - v_y^2)\hat{k} =$ constant.
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