Question

Two forces of 4 N and 3 N act on a particle. For maximum resultant force, the angle between them should be-

• A. \(180^\circ\)
• B. \(120^\circ\)
• C. \(90^\circ\)
• D. \(0^\circ\)

Hint:

Maximum resultant of two forces is obtained when they act in the same direction. Minimum resultant is obtained when they act in opposite directions.

Answer 1

The Correct Option is D

Concept: According to the parallelogram law of vector addition, the resultant of two forces \(F_1\) and \(F_2\) acting at an angle \(\theta\) is \[ R=\sqrt{F_1^2+F_2^2+2F_1F_2\cos\theta} \] Given: \[ F_1=4N \] \[ F_2=3N \]

Step 1: Substitute the given values. \[ R = \sqrt{4^2+3^2+2(4)(3)\cos\theta} \] \[ R = \sqrt{25+24\cos\theta} \]

Step 2: Find the condition for maximum resultant. Since \(25\) is constant, \(R\) will be maximum when \(\cos\theta\) is maximum. The maximum value of cosine is \[ \cos0^\circ=1 \] Therefore, \[ \theta=0^\circ \]

Step 3: Verify the resultant. \[ R = \sqrt{25+24} = \sqrt{49} = 7N \] Hence, the maximum resultant occurs when the two forces act in the same direction.