Question

Three forces are acting on a particle in which \( F_1 \) and \( F_2 \) are perpendicular. If \( F_1 \) is removed, find the acceleration of the particle.

• A. \( \frac{F_2}{m} \)
• B. \( \frac{F_1}{m} \)
• C. \( \frac{F_1 + F_2}{m} \)
• D. \( \sqrt{\left(\frac{F_1}{m}\right)^2 + \left(\frac{F_2}{m}\right)^2} \)

Hint:

When forces are perpendicular, the resultant acceleration due to two forces can be calculated using the Pythagorean theorem. However, if one force is removed, the remaining acceleration depends solely on the remaining force.

Answer 1

The Correct Option is A

Given that \( F_1 \) and \( F_2 \) are perpendicular, the particle is under the influence of two forces. When \( F_1 \) is removed, the only force acting on the particle is \( F_2 \). The acceleration of the particle due to the force \( F_2 \) is given by Newton's second law: \[ a = \frac{F_2}{m} \] Where: - \( F_2 \) is the remaining force acting on the particle, - \( m \) is the mass of the particle. Thus, the acceleration of the particle is \( \frac{F_2}{m} \).