Question

Two equal forces acting at a point with an angle of 60° between them, if the resultant is equal `30sqrt(3)N`, the magnitude of the force will be

Options

• 20 N

• 0

• 30 N

• 60 N

Answer 1

30 N

Explanation:

Given, F₁ = F₂ = F  ......(Say)

R = `30sqrt(3)` N and θ = 60°

The resultant force on the body.

R = `sqrt(F_1^2 + F_2^2 + 2F_1F_2  cos theta)`

`30sqrt(3) = sqrt(F^2 + F^2 + 2F^2  cos 60^circ)`

= `sqrt(2F^2 + 2F^2 xx 1/2)`

`30sqrt(3) = sqrt(3F^2) = sqrt(3)F`

F = 30 N = F₁ = F₂.