Question

Three force F₁ = 10N, F₂ = 8 N, F₃ = 6N are acting on a particle of mass 5 kg. The forces F₂ and F₃ are applied perpendicular so that particle remains at rest. If the force F₁ is removed, then the acceleration of the particle is

• A. 2 ms^-2
• B. 7 ms^-2
• C. 4.8 ms^-2
• D. 0.5 ms^-2

Answer 1

The Correct Option is A

To find the acceleration of the particle when the force F_1 is removed, let's solve the problem step-by-step:

1. Given forces are F_1 = 10\, \text{N}, F_2 = 8\, \text{N}, and F_3 = 6\, \text{N}.
2. The particle remains at rest under the action of all three forces. This implies that the net force acting on it is zero due to equilibrium.
3. For equilibrium, the resultant force by F_2 and F_3 must counteract F_1.
   Since F_2 and F_3 are perpendicular to each other, we use the Pythagorean theorem to find their resultant:
4. F_{\text{resultant}} = \sqrt{F_2^2 + F_3^2}
   = \sqrt{8^2 + 6^2}
   = \sqrt{64 + 36} = \sqrt{100} = 10\, \text{N}.
5. This resultant force F_{\text{resultant}} of 10 N counteracts F_1 exactly to keep the particle in equilibrium.
6. When F_1 is removed, the particle is only influenced by the resultant force of F_2 and F_3, which is 10 N.
7. Using Newton's second law, the acceleration a can be calculated as: F = ma, hence a = \frac{F}{m}.
8. Substituting the values, we get:
   a = \frac{10\, \text{N}}{5\, \text{kg}} = 2\, \text{ms}^{-2}.

The correct answer is 2\, \text{ms}^{-2}.