Laws Of Motion Question 263
Question: A particle moves in the xy-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 pat time t is [MP PET 1996; UPSEAT 2000]
Options:
A) $ 90{}^\circ $
B) $ 0{}^\circ $
C) $ 180{}^\circ $
D) $ 30{}^\circ $
Show Answer
Answer:
Correct Answer: A
Solution:
Given that $ \vec{p}=p _{x}\hat{i}+p _{y}\hat{j}=2\cos t\ \hat{i}+2\sin t\ \hat{j} $
$ \vec{F}=\frac{d\vec{p}}{dt}=-2\sin t\ \hat{i}+2\cos t\ \hat{j} $
Now, $ \vec{F}.\vec{p}=0 $ i.e. angle between $ \vec{F}\ \text{and }\vec{p}\ $ is 90°.
