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The resultant of two forces P and Q is R. If Q is double the new resultant becomes perpendicular to P. Prove that P =R by triangle law.


Azhar aftab 29th Mar, 2019
Answer (1)
Debosmitha Bhattacharyya Student Expert 29th Mar, 2019

Hello Azhar,

Resultant of two forces P and Q is R


R = P + Q


|R| = sqrt(P^2 + Q^2 + 2PQCosθ)


When Q is doubled new resultant R’ is


R’ = P + 2Q


Since it is perpendicular to P, the dot product of R’ and P is zero


(R’).(P) = 0


(P + 2Q).(P) = 0


P^2 + 2PQCosθ = 0


(Dot product of P and P is P^2 and that of P and 2Q is 2PQCosθ)


Cosθ = -P/(2Q)


R = sqrt(P^2 + Q^2 + 2PQCosθ)


R = sqrt(P^2 + Q^2 + 2PQ*(-P/(2Q))


R = sqrt(P^2 + Q^2 - P^2)


R = Q

Hope this helps.

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