MCQ
The horizontal force and the force inclined at an angle ${60^o}$ with the vertical, whose resultant is in vertical direction of $ P $ $kg$, are
- A$P, 2P$
- B$P,\,\,P\sqrt 3 $
- ✓$2P,\,\,P\sqrt 3 $
- DNone of these
✓
Answer
Correct option: C.
$2P,\,\,P\sqrt 3 $
c
(c) Let $\overrightarrow {OA} = {P_1}i,$ $\overrightarrow {CB} = - {P_1}i,$
(c) Let $\overrightarrow {OA} = {P_1}i,$ $\overrightarrow {CB} = - {P_1}i,$
$\overrightarrow {OB} = - {P_1}i + Pj$
$\frac{{\overrightarrow {OB} \,.\,j}}{{OB}} = \cos 60^\circ \Rightarrow \frac{{( - {P_1}i + Pj)\,.\,j}}{{\sqrt {P_1^2 + {P^2}} }} = \frac{1}{2}$
$ \Rightarrow 2P = \sqrt {{P^2} + P_1^2} \Rightarrow {P_1} = P\sqrt 3 $
$|\overrightarrow {OB} |\, = \sqrt {{P^2} + P_1^2} = \sqrt {{P^2} + 3{P^2}} = 2P.$
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