F1 and F2 at θ1
Fnet1=P2+Q2+P2+Q2+2(P2+Q2)cosθ1
Fnet2=P2+Q2+P2+Q2+2(P2+Q2)cosθ2
If Fnet1=3(P2+Q2)=2(P2+Q2)+2(P2+Q2)cosθ1
⇒cosθ1=2(P2+Q2)P2+Q2
⇒θ1=60∘
Fnet2=2(P2+Q2)=2(P2+Q2)+2(P2+Q2)cosθ2
⇒cosθ2=0⇒θ2=90∘
Statement-I : Two forces (P+Q) and (P−Q) where P⊥Q, when act at an angle θ1 each other, the magnitude of their resultant is 3(P2+Q2), when they act at an angle θ2, the magnitude of their resultant becomes 2(P2+Q2). This is possible only when θ1<θ2.
Statement-II : In the situation given above.
θ1=60∘ and θ2=90∘
In the light of the above statement, choose the most appropriate answer from the options given below :
Held on 31 Aug 2021 · Verified 6 Jul 2026.
Statement I is false but Statement II is true.
Both Statement I and Statement II are true.
Both Statement I and Statement II are false.
Statement I is true but Statement II is false.
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