A particle moves in the x-y plane under the action of a force F s… - Vidyadip

MCQ

A particle moves in the $x-y$ plane under the action of a force $\overrightarrow F $ such that the value of its linear momentum $(\overrightarrow P )$ at anytime t is ${P_x} = 2\cos t,\,{p_y} = 2\sin t.$ The angle $\theta $between $\overrightarrow F $ and $\overrightarrow P $ at a given time $t$. will be $\theta =$ ........... $^o$

A
$0$
B
$30$
✓
$90$
D
$180$

✓

Answer

Correct option: C.

$90$

c
(c) ${P_x} = 2\cos t$, ${P_y} = 2\sin t$ $⇒$$\vec P = 2\cos t\;\hat i + 2\sin t\;\hat j$

$\vec F = \frac{{d\vec P}}{{dt}} = - 2\sin t\;\hat i + 2\cos t\;\hat j$

$\vec F.\vec P = 0$ $⇒$ $\theta = 90^\circ $

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