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Q.

The resultant of two forces 2P and $\sqrt{2} P$ is $\sqrt{10} P$ . The angle between the forces is

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a

60⁰

b

30⁰

c

45⁰

d

90⁰

answer is C.

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Detailed Solution

$\sqrt{10} P = \sqrt{4 P^{2} + 2 P^{2} + 4 \sqrt{2} P^{2} \cos θ}$

$\Rightarrow 10 P^{2} = (6 + 4 \sqrt{2} \cos θ) P^{2}$

$\Rightarrow \cos θ = \frac{1}{\sqrt{2}}$

$\Rightarrow θ = 45^{o}$

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The resultant of two forces 2P and 2P is 10P. The angle between the forces is