Question

A particle moves is $X-Y$ plane under the influence of a force $F$ such that its instantaneous momentum is $ P = i^2 \cos \,t + j^2\sin\,t$, what is the angle between the force and instantaneous momentum?

• A. $ 0^{\circ} $
• B. $ 180^{\circ} $
• C. $ 90^{\circ} $
• D. $ 45^{\circ} $

Answer 1

Answer: (C)

Here, $p = i^2 \cos t + j^2 \cos t $
$ F \frac{d p}{d t}=-2 i \sin t+2 j \cos t$
$F \cdot P=(-2 i \sin t+2 j \cos t) \cdot(2 i \cos t+j \sin t)$
$=-4 \sin t \cos t=+4 \sin t \cos t=0$
Therefore, $\theta=90^{\circ}$