Question

P and Q are two forces of equal magnitude acting at a point O at such an angle that their resultant R has a magnitude equal to that of P . If the magnitude of P is doubled then find the angle between the new resultant R1 and Q.

Answer 1

Answer:

Explanation: Here P , Q and R in magnitude are equal according to the question,

So, we can write,

R^2 = P^2 + Q^2 + 2PQcos theta

P^2 = P^2 + P^2 + 2P^2 cos theta      [Acc. to the question]

After solving,

-1/2 = cos theta

cos 120 = cos theta

Therefore, theta = 120

Again, the new angle between R1 and Q be ∅ when P is doubled is,

We have from Parallelogram law,

Tan∅ = $\frac{Psin theta}{P+Qcos theta}$

Tan∅ =  2Q sin 120 / 2Q + Qcos 120

After putting theta value we get,

Tan∅ = ∞

Therefore,∅ =90 degree.