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Two forces F1 and F2 acting on a body have a resultant R, if F2 is doubled the new resultantis Rforms are right angle with F. Prove that R, and F2 have the same magnitude. |
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Answer» Let θ be the angle betweenf1andf2 (Quantities in bold represents vectors) Given, f1+f2=r1----- 1 f1+ 2f2=r2 ----2 Taking dot product on itself of eqn. 1 r1. r1=f1.f1+f1.f2+f2.f1+f2.f2 => r12= f12+ f22+ 2f1f2cosθ ---3. Taking dot product off1with eqn. 2 f1.(f1+ 2f2)=f1.r2 Since,f1andr2are perpendicular to each otherf1.r2= 0 => f12+ 2f1f2cosθ = 0 ---4. By eqn. 3 and 4. r12= (f12+ 2f1f2cosθ) + f22 => r12= 0 + f22 => r1= f2 QED. |
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