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Question: Answered & Verified by Expert
With two forces acting at a point, the maximum effect is obtained when their resultant is $4 \mathrm{~N}$. If they act at right angles, then their resultant is $3 \mathrm{~N}$. Then the forces are
MathematicsVector AlgebraJEE MainJEE Main 2004
Options:
  • A
    $(2+\sqrt{2}) N$ and $(2-\sqrt{2}) N$
  • B
    $(2+\sqrt{3}) \mathrm{N}$ and $(2-\sqrt{3}) \mathrm{N}$
  • C
    $\left(2+\frac{1}{2} \sqrt{2}\right) \mathrm{N}$ and $\left(2-\frac{1}{2} \sqrt{2}\right) \mathrm{N}$
  • D
    $\left(2+\frac{1}{2} \sqrt{3}\right) \mathrm{N}$ and $\left(2-\frac{1}{2} \sqrt{3}\right) \mathrm{N}$
Solution:
1645 Upvotes Verified Answer
The correct answer is:
$\left(2+\frac{1}{2} \sqrt{2}\right) \mathrm{N}$ and $\left(2-\frac{1}{2} \sqrt{2}\right) \mathrm{N}$
$P+Q=4, P^2+Q^2=9 \Rightarrow P=\left(2+\frac{1}{2} \sqrt{2}\right) N$ and $Q=\left(2-\frac{1}{2} \sqrt{2}\right) N$

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