Question

The force whose magnitude are in the ratio of3:5 gives resultant 35N If the angle of inclinationi s60 degree then find the magnitude of each force

Answer 1

Given ,

• The ratio of magnitudes of two forces = 3 : 5
• The resultant force = 35 N
• The angle b/w two forces = 60

Let , the magnitude of two forces be 3n and 5n

We know that , the resultant between two vectors is given by

$\sf \fbox{R = \sqrt{ {(p)}^{2} + {(q)}^{2} + 2pqcos( \theta) }}$

Thus ,

$\sf \mapsto 35 = \sqrt{ {(3n)}^{2} + {(5n)}^{2} + 2 \times 3n \times 5n \times cos(60)} \\ \\ \sf \mapsto {(35)}^{2} = 9 {n}^{2} + 25 {n}^{2} + \frac{30 {n}^{2} }{2} \\ \\ \sf \mapsto 1225 =49 {n}^{2} \\ \\ \sf \mapsto {n}^{2} = \frac{1225}{49} \\ \\ \sf \mapsto {n}^{2} = 25 \\ \\ \sf \mapsto n = 5$

$\therefore\sf \underline{The \: magnitude of \: two \: forces \: are \: 15 \: N \: and \: 25 \: N}$