Question

A particle moves in x-y plane under the action of a force $\overrightarrow{F}$ such that the value of its linear momentum $\overrightarrow{p}$ at any time t is p_x = 2cost, p_y = 2sint. The angle between $\overrightarrow{F}$and $\overrightarrow{p}$ at given time t will be

• A. θ = 0⁰
• B. θ = 30⁰
• C. θ = 90⁰
• D. θ = 180⁰

Answer 1

Answer: (C)

θ = 90⁰

Answer 2

P = $\sqrt{P_{x}^{2} + P_{y}^{2}}$ = 2$\sqrt{\cos^{2}t + \sin^{2}t}$ = 2, which is

independent of t, which means the applied force is not changing the magnitude of velocity.

i.e. $\overrightarrow{F}$ is perpendicular to $\overrightarrow{p}$

Hence (3) is correct.