Question

A body of mass 10 kg is acted upon by two perpendicular forces, 6 N and 8 N. The resultant acceleration of the body is ______.

1. 1 m s^–2 at an angle of tan⁻¹ `(4/3)` w.r.t 6 N force.
2. 0.2 m s^–2 at an angle of tan⁻¹ `(4/3)` w.r.t 6 N force.
3. 1 m s^–2 at an angle of tan⁻¹ `(3/4)` w.r.t 8 N force.
4. 0.2 m s^–2 at an angle of tan⁻¹ `(3/4)` w.r.t 8 N force.

Answer 1

a and c

Explanation:

Consider the adjacent diagram

Given, mass = m = 10 kg

F₁ = 6 N, F₂ = 8 N

Resultant force = F = `sqrt(F_1^2 + F_2^2)`

= `sqrt(36 + 64)`

= 10 N

a = `F/m = 10/10` = 1 m/s²; along R.

Let θ₁ be the angle between R and F₁.

tan θ₁ = `8/6 = 4/3`

θ₁ = `tan^-1 (4/3)` w.r.t. F₁ = 6 N

Let θ₂ be the angle between F and F₂.

tan θ₂ = `6/8 = 3/4`

θ₂ = `tan^-1 (3/4)` w.r.t. F₂ = 8 N