Question

A particle moves in the x – y plane under the influence of a force such that its linear momentum is $p\left(t\right)=A\left[\hat{i}cos\right(kt)-\hat{j}sin(kt\left)\right]$, where A and k are constants. The angle between the force and the momentum is

• A. $0^{\circ }$
• B. ${30}^{\circ }$
• C. ${45}^{\circ }$
• D. ${90}^{\circ }$

Answer 1

The correct option is D

${90}^{\circ }$

$\overrightarrow{p}\left(t\right)=A\left[\hat{i}cos\right(kt)-\hat{j}sin(kt\left)\right]\Rightarrow \overrightarrow{F}\left(t\right)=\frac{d\overrightarrow{p}\left(t\right)}{dt}=Ak[-\hat{i}sin(kt)-\hat{j}cos(kt\left)\right]$
Now, finding the dot product, $\overrightarrow{p}\left(t\right).\overrightarrow{F}\left(t\right)=0$
Hence, angle is ${90}^{\circ }$.