Question

Three forces P, Q & R are acting at a point in a
plane. The angle between P and Q, Q and R are
150° and 120° respectively. Then for equilibrium,
forces P, Q & R are in the ratio :
(1)1:2:3
(2) 1:2:
(3)3:2:1
(4) 31/2: 2:1
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Answer 1

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Explanation:

1.Draw  the  diagram  to  represent  P,  Q  and  R  in  the  plane,  say  OPQR,  with  O  as  origin  and  OP

2.Along X- axis say. O is initial point and P is terminal point for the vector P.

for other vectors Q and R.

The he angle ROP = 360(-(150+120) = 90°

Represent vector R or OR as PR', so that the line segment PR' is parallel to OR.

By triangle law P+R = OR'

OR' must be opposite and equal to Q in order to keep the

particle at O in equilibrium.

Hence, angle POR' = 30.

Let |P|, |Q| |R | bet the respective magnitudes.

Apply sine rule to for triangle OPR'

OR =|R|/sin30=|P|/sin60=|Q|

|P|/1=|Q|/2=|R|/√3

hence , ratio=1:2:√3

Answer 2

Answer:

the answer of this question is an