Question

When forces F1​, F2​, and F3​ are acting on a particle of mass m such that F2​ and F3​ are mutually perpendicular, then the particle remains stationary. If the force F1​ is now removed, then the acceleration of the particle is:

a. F1/m​​
b. ​F2​F3/mF1​​
c. F2​−F3/m​​
d. F2/m​​

Answer 1

Correct option: a. F1/m​​

When F1 is removed, the particle accelerates due to the mutual perpendicular forces F2 and F3. The resultant force equals F1, thus the acceleration is calculated using Newton's second law, giving the answer as F1/m.

Step-by-step explanation:

The scenario presents a particle that is stationary under the influence of three forces.

When F1 is removed, the particle will begin to accelerate due to the remaining forces, F2 and F3​, which are mutually perpendicular.

To find the acceleration of the particle, we calculate the resultant force from F2 and F3 using vector addition, since the forces are perpendicular:

• The resultant force (Fr) is the square root of (F22 + F32).

Since F1 was holding the particle stationary, F1 is equal in magnitude to the resultant force, but opposite in direction. The magnitude of the acceleration (a) of the particle after F1 is removed can be found using Newton's second law, Fr = m * a:

• a = Fr / m

However, because F2 and F3 are the only forces acting and they are perpendicular, the magnitude of Fr is equal to F1. Thus the acceleration can be simplified to:

• a = F1 / m

The correct answer is that the acceleration of the particle is F1 / m.