Question

The resultant of two forces acting on the same point simultaneously will be the greatest when the angle between them is:a) 180 degrees

b) 45 degrees
c) 0 degrees
d) 90 degrees

Answer 1

0 degrees

Step-by-step explanation:

Let
`F_1\ and\ F_2` are two forces. The resultant of two forces acting on the same point is given by :

`F_R=√(F_1^2+F_2^2+2F_1F_2\ cos\theta)`

Where
`\theta` is the angle between two forces

When
`\theta=0` i.e. when two forces are parallel to each other,

`F_R=√(F_1^2+F_2^2+2F_1F_2\ cos(0))`

`F_R=√(F_1^2+F_2^2+2F_1F_2)`

When
`\theta=90^(\circ)` i.e. when two forces are parallel to each other,

`F_R=√(F_1^2+F_2^2+F_1F_2\ cos(90))`

`F_R=√(F_1^2+F_2^2)`

When
`\theta=180^(\circ)` i.e. when two forces are parallel to each other,

`F_R=√(F_1^2+F_2^2+F_1F_2\ cos(180))`

`F_R=√(F_1^2+F_2^2-2F_1F_2)`

It is clear that the resultant of two forces acting on the same point simultaneously will be the greatest when the angle between them is 0 degrees. Hence, this is the required solution.