Question

A particle moves in the X-Y plane under the influence of a force such that its linear momentum is $p(t) =A[\widehat{i}cos\, (kt) -\widehat{j}sin\, (kt)]$ 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

Answer: (D)

$90^\circ$

Answer 2

$\, \, \, \, \, \, \, F=\frac{dp}{dt} =-kA\, sin\, (kt) \widehat{i} - kA\, cos\, (kt)\widehat{j}$
$\, \, \, \, \, \, \, p=A\, cos\, (kt) \widehat{i} - A\, sin\, (kt)\widehat{j}$
Since, \hspace20mm F.p=0
$\therefore$ Angle between F and p should be $90^\circ.$