Question

12. Three forces of equal magnitudes and making an angle of 120° with each other act on a body. Then that the resultant force is (A) Zero (B) 10N (C) 20N (D) 30N​

Answer 1

$\tt\blue{\underline{Answer:}}$

$\tt\green{\therefore{F_{net}=0\:N}}$

$\tt\orange{\underline{Step-by-step\:\:explanation:}}$

$\tt\green{\underline{Given :}} \\ \tt: \implies Angle \: between \: forces = 120 \degree \\ \\ \tt: \implies Magnitude \: of \: all \: forces \: are \: same \\ \\ \tt\red{\underline{To \: Find:}} \\ \tt: \implies F_{net} = ?$

• According to given question :

$\bold{a As \: we \: know \: that} \\ \tt: \implies Component \: of \: AO=F\:sin \theta \: and \: F \: cos \theta \\ \\ \bold{similarly} \\ \tt: \implies Component \: of \: BO = F \: sin \theta \: and \: F\: cos \theta \\ \\ \sf Where \: \: \theta = 30 \degree (draw \: x \: and \: y \: axis \: then \: 120 - 90 = 30 \degree) \\ \\ \because \sf F\: sin \theta \: is \: in \: same \:direction \: with \: same \: sign \\ \because \sf F\: cos \theta \: is \: in \: opposite \: direction \: with \: same \: sign \\ \\ \tt \implies So, \: F\: cos \theta - F \: cos \theta = 0 \\ \\ \tt: \implies F\: sin \theta + F \: sin \theta = 2f \: sin \theta \\ \\ \bold{As \:through \: given \: diagram} \\ \tt: \implies F_{net} = 2F \: sin \theta - F \\ \\ \tt: \implies F_{net} =2F \times sin \: 30 \degree - F \\ \\ \tt: \implies F_{net} =2F \times \frac{1}{2} - F \\ \\ \tt: \implies F_{net} =F - F \\ \\ \green{\tt: \implies F_{net} =0 \: N}$