Problem Statement: Two forces of equal magnitude acting on a particle. The angle between forces is 60. The resultant force on the particle is?

Solution:

To find the resultant force on the particle, we need to use the concept of vector addition. We can add two vectors graphically by placing the tail of one vector at the head of the other vector. The resultant vector is then drawn from the tail of the first vector to the head of the second vector.

Step 1: Draw a diagram of the forces

First, draw a diagram of the two forces. Let's assume that each force has a magnitude of F.



Step 2: Resolve the forces into their components

Next, we need to resolve the forces into their components. Let's call the forces F1 and F2, where F1 is the force that makes an angle of 60 degrees with the x-axis, and F2 is the force that makes an angle of 120 degrees with the x-axis.



Step 3: Find the x and y components of the forces

Using trigonometry, we can find the x and y components of the forces.

F1x = F cos(60) = F/2

F1y = F sin(60) = F√3/2

F2x = F cos(120) = -F/2

F2y = F sin(120) = F√3/2

Step 4: Add the x and y components of the forces

Now we can add the x and y components of the forces to find the resultant force.

Rx = F1x + F2x = F/2 - F/2 = 0

Ry = F1y + F2y = F√3/2 + F√3/2 = F√3

Therefore, the magnitude of the resultant force is F√3, and the direction of the resultant force is 60 degrees above the x-axis.

Conclusion:

The resultant force on the particle is F√3 and the direction of the resultant force is 60 degrees above the x-axis.

F√3 is the correct answer as-
F²+F²+2F*Fcos60=R²
F²+F²+F²=R²
3F²=R²
F√3=R²