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

Step 1: Understand the question.
Two forces, 4 N and 3 N, act on one particle. We want the angle between them that gives the largest possible total (resultant) force.

Step 2: Write the resultant formula.
For two forces $F_1$ and $F_2$ at an angle $\theta$, the resultant is $R = \sqrt{F_1^2 + F_2^2 + 2F_1F_2\cos\theta}$.

Step 3: Put in the values.
$R = \sqrt{4^2 + 3^2 + 2(4)(3)\cos\theta} = \sqrt{25 + 24\cos\theta}$.

Step 4: Find when R is largest.
Since 25 is fixed, $R$ grows when $\cos\theta$ is largest. The largest value of cosine is 1, and that happens when $\theta = 0^\circ$.

Step 5: Picture why.
When $\theta = 0^\circ$, both forces point the same way, so they simply add up: $4 + 3 = 7\ N$. Any other angle makes them partly cancel.

Step 6: Check other options and conclude.
At $90^\circ$ we get $R = 5\ N$, at $120^\circ$ even less, and at $180^\circ$ they oppose giving only 1 N. So the maximum resultant is at $0^\circ$.
\[ \boxed{\text{$0^\circ$}} \]