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Question

Two forces P and Q act such that the resultant R is equal to the magnitude of P. If P is doubled, what is the angle made by the new resultant with the force Q?

A
0
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B
30
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C
60
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D
90
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Solution

The correct option is D 90

R=P2+Q2+2PQcos θ
where θ is the angle between P and Q
According to question,
P2=P2+Q2+2PQcos θ
Q2+2PQcos θ=0
Q(Q+2Pcos θ)=0...(1)
If α is the angle made by the new resultant with Q then,
tan α=2Psin θQ+2Pcos θ
Using equ. (1), we can say
tan α=2Psin θ0
α=900

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