Question

8: Two forces 20N and 5N are acting at an angle of 120° between them. The resultant force is
a) 16.03N
b) 18.03N
c) 21N
d) None of these​

Answer 1

$\sqrt{ {20}^{2} + {5}^{2} + 2 \times 20 \times 5 \: cos120 } \\ = \sqrt{400 + 25 + 200 \times - 0.5} \\ = \sqrt{325} \\ = 18.03 \: newton$

Answer 2

b) 18.03 N

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$\orange{\bigstar}$  Given  $\green{\bigstar}$

Two forces 20 N and 5 N are acting at an angle of 120° between them

$\orange{\bigstar}$  To Find  $\green{\bigstar}$

Resultant force

$\orange{\bigstar}$  Knowledge required  $\green{\bigstar}$

$\bf \red{R=\sqrt{F_1^2+F_2^2+2F_1F_2.cos\theta}\ \; \bigstar}$

where

• R denotes resultant force
• F₁ denotes Force 1
• F₂ denotes Force 2
• θ denotes angle between F₁ and F₂

$\orange{\bigstar}$  Solution  $\green{\bigstar}$

Given ,

• F₁ = 20 N
• F₂ = 5 N
• θ = 120°
• R = ? N

Apply formula ,

$\bf \blue{R=\sqrt{F_1^2+F_2^2+2F_1F_2.cos\theta}}\\\\\to \rm R=\sqrt{(20)^2+(5)^2+2(20)(5).cos(120)}\\\\\to \rm R=\sqrt{400+25+200\left(-\dfrac{1}{2}\right)}\\\\\to \rm R=\sqrt{425-100}\\\\\to \rm R=\sqrt{325}\\\\\to \bf R=18.027\\\\\to \bf R \cong 18.03\ \; \pink{\bigstar}$

So , Option B is correct

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