Question

A body of mass 2 kg is acted upon by two forces each of magnitude 1 N and inclined at 60° with each other. The acceleration of the body in m/s is ____________. [cos 60° = 0.5]

विकल्प

• `sqrt(0.75)`

• `sqrt(0.65)`

• `sqrt(0.20)`

• `sqrt(0.35)`

Answer 1

A body of mass 2 kg is acted upon by two forces each of magnitude 1 N and inclined at 60° with each other. The acceleration of the body in m/s is `underline(sqrt(0.75))`.

Explanation:

Given, F₁ = F₂ = 1 N, m = 2 kg and θ = 60°

Resultant force, F = `sqrt("F"_1^2 + "F"_2^2 + 2"F"_1"F"_2 cos θ)`

= `sqrt(1^2 + 1^2 + 2 cos 60°)`

= `sqrt(2 + 2(0.5))`

= `sqrt3` N

ma = `sqrt3`

or a = `sqrt3/"m" = sqrt3/2 = sqrt(3/4) = sqrt0.75  "ms"^-2`