UPSEE 2018 Solved Paper

We have two forces is 3P and 2P, let angle between two forces is θ.
∴ Resultant R=√(3P)2+(2P)2+12P2‌cos‌θ
=√P2(13+12‌cos‌θ) .......(i)
Now first force is doubled.
∴ First force =6P
and resultant is also double
∴R=2R
⇒2R=√(6P)2+(2P)2+24P2‌cos‌θ
⇒2R=√P2(40+24‌cos‌θ) .........(ii)
From Eqs. (i) and (ii),
2P√13+12‌cos‌θ=P√40+24‌cos‌θ
⇒4(13+12‌cos‌θ)=40+24‌cos‌θ
⇒52+48‌cos‌θ=40+24‌cos‌θ
⇒24‌cos‌θ=−12
⇒cos‌θ=−

1

2

⇒θ=120°