The resultant of two forces having magnitude 3p and 2p is R. If the force having magnitude 3p is doubled keeping the same direction, then the resultant is also doubled. The angle between two forces is
A
120o
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
B
150o
No worries! We‘ve got your back. Try BYJU‘S free classes today!
C
180o
No worries! We‘ve got your back. Try BYJU‘S free classes today!
D
125o
No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution
The correct option is A120o Let θ be the angle between two forces. We know resultant of two forces F1 and F2 inclined at an angle θ is given by R=√F21+F22+2F1F2cosθ
Or R2=F21+F22+2F1F2cosθ(1)
Here F1=3p and F2=2p ∴R2=(3p)2+(2p)2+2×3p×2pcosθ
or R2=9p2+4p2+12p2cosθ R2=13p2+12p2cosθ(2)
Now F1=2×3p=6p,R=2R,F2=2p ∴ From equation (1), (2R)2=(6p)2+(2p)2+2×6p×2pcosθ 4R2=36p2+4p2+24p2cosθ 4R2=40p2+24p2cosθ
or R2=10p2+6p2cosθ(3)
equating (2) and (3), we get, 13p2+12p2cosθ=10p2+6p2cosθ
Or 3p2=−6p2cosθcosθ=−12 ∴θ=cos−1(−12)=120∘ ∴θ=120∘