Question

A particle moves in the $x y$-plane under the action of a force $F$ such that the components of its linear momentum $p$ at any time $t$ are $p_{x}=2 \cos t, p_{y}=2 \sin t$. The angle between $F$ and $p$ at time $t$ is

• A. $90^{\circ}$
• B. $0^{\circ}$
• C. $180^{\circ}$
• D. $30^{\circ}$

Answer 1

Answer: (A)

Given that $\vec{p}=p_{x} \hat{i}+p_{y} \hat{j}$
$=2 \cos t \hat{i}+2 \sin t \,\hat{j}$
$\therefore \vec{F}=\frac{d \vec{p}}{d t}=-2 \sin t \hat{i}+2 \cos t \hat{j}$
Now, $\vec{F} \cdot \vec{p}=0$ i.e. angle between $\vec{F}$ and $\vec{p}$ is $90^{\circ}$.