Question

3. Two forces of equal magnitude of 100 N are acting on a particle
simultaneously at an angle of 120°. The magnitude of resultant force is
a. 100 N
b. 200 N
C. 400 N
d. 500 N​

Answer 1

Given :-

Two forces have equal magnitude ; let,

• | A | = 100 N
• | B | = 100 N

Angle between Forces A and B is , x = 120°

To find :-

Magnitude of the resultant force, | R | = ?

Formula to be used :-

Formula for resultant of two vectors

• |R| = √( |A|^2 + |B|^2 + 2 |A| |B| cos x)

[ where |R| is magnitude of resultant of two vectors A and B and x is the angle between vectors A and B ]

Calculation :-

Using formula for magnitude of resultant

➠ |R| = √( |A|^2 + |B|^2 + 2 |A| |B| cos x)

➠ |R| = √{ (100)^2 + (100)^2 + 2 (100) (100) cos 120° }

➠ |R| = √( 2 (100)^2 + 2 (100)^2 cos 120° )

➠ |R| = √{ 2 (100)^2 ( 1 + cos 120° ) }

➠ |R| = 100√2 √( 1 + cos 120° )

[ putting value of cos 120° ]

➠ |R| = 100 √2 √( 1 + (-1/2) )

➠ |R| = 100 √2 × ( 1/√2 )

➠ |R| = 100 N

therefore,

magnitude of Resultant vector will be 100 N.