Question

9.The resultant of two forces P and Q is of magnitude P.Prove that if P is doubled, the resultant force will

be perpendicular to Q.
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Answer 1

Answer:

Square of Resultant R is R^2 = P^2 + Q^2 + 2PQ cos α,

α is the angle between P and Q.

tan θ = Q sin α / ( P + Q cosα), θ is the angle between R and P.

If Q is doubled , and if the angle between P and the new resultant S is 90 °,

tan 90 = 2Q sin α / ( P + 2Q cosα),=infinity.

Therefore, P = - 2Q cosα.

But R^2 = P^2 + Q^2 + 2PQ cos α,

R^2 = P^2 + Q^2 - P^2

R^2 = Q^2

R = Q ( in magnitude)