Question

The magnitude and direction of the acceleration produced in a body of mass 5 kg when two mutually perpendicular forces 8 N and 6 N act on it, are respectively:

• A. 2 m s⁻²; $\tan^{-1}(4/3)$ with 8 N force
• B. 2 m s⁻²; $\tan^{-1}(3/4)$ with 8 N force
• C. 2 m s⁻²; $\tan^{-1}(3/4)$ with 6 N force
• D. 20 m s⁻²; $\tan^{-1}(4/3)$ with 8 N force

Hint:

Always associate the denominator in the $\tan \theta$ formula with the force from which you are measuring the angle. Angle with 8 N $\rightarrow$ 8 is in the denominator.

Answer 1

The Correct Option is B

Step 1: Understanding the Concept:
Forces are vectors. When multiple forces act on a body, we must find the resultant (net) force to calculate acceleration using Newton's Second Law ($F = ma$).

Step 2: Key Formula or Approach:
1. Resultant Force ($F_{net}$) for perpendicular vectors: $\sqrt{F_1^2 + F_2^2}$ 2. Acceleration ($a$) = $F_{net} / m$ 3. Direction ($\theta$) with respect to $F_1$: $\tan \theta = F_2 / F_1$

Step 3: Detailed Explanation:
Given: $m = 5$ kg, $F_1 = 8$ N, $F_2 = 6$ N. 1. Calculate Net Force: \[ F_{net} = \sqrt{8^2 + 6^2} = \sqrt{64 + 36} = \sqrt{100} = 10 \text{ N} \] 2. Calculate Acceleration: \[ a = \frac{10}{5} = 2 \text{ m/s}^2 \] 3. Calculate Direction with respect to 8 N force: \[ \tan \theta = \frac{6}{8} = \frac{3}{4} \implies \theta = \tan^{-1}(3/4) \]

Step 4: Final Answer:
The acceleration is 2 m s⁻² at an angle of $\tan^{-1}(3/4)$ with the 8 N force.