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The resultant of two forces P1 and P2 is R. If P1 is doubled and the new resultant remains R and becomes perpendicular to P2 ,then

The resultant of two forces P1 and P2 is R. If P1 is doubled and the new resultant remains R and becomes perpendicular to P2 ,then 
 

Grade:12th pass

1 Answers

Arun
25763 Points
3 years ago

Dear student
I have replaced P1 and P2 by P and Q
Resultant of two forces P and Q is R
R = P + Q
|R| = sqrt(P2 + Q2 + 2PQCosθ)
When Q is doubled new resultant R’ is
R’ = P + 2Q
Since it is perpendicular to P, 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(P2 + Q2 + 2PQCosθ)
R = sqrt(P2 + Q2 + 2PQ*(-P/(2Q))
R = sqrt(P2 + Q2 - P2)
R = Q
Regards Arun
(askIITians forum expert)

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