Given: Angle between two forces = 120 degrees, Resultant force = 10 kg wt, Resultant force is perpendicular to one of the forces

To find: Magnitude of one of the forces

Solution:

Step 1: Draw a diagram

Draw a diagram of the given situation. Label the forces as F1 and F2, and the resultant force as R. Make sure to include the angle between F1 and F2.

Step 2: Use the law of cosines

Use the law of cosines to find the magnitude of one of the forces. The law of cosines states that:

c² = a² + b² - 2ab cos(C)

Where c is the length of the side opposite to angle C, and a and b are the lengths of the other two sides.

In this case, we know the length of the resultant force R, and we know that it is perpendicular to one of the forces (let's say F1). Therefore, the angle between R and F2 is 60 degrees (since the angle between F1 and F2 is 120 degrees). Using the law of cosines, we get:

R² = F1² + F2² - 2F1F2 cos(60)

Substituting R = 10 and cos(60) = 1/2, we get:

100 = F1² + F2² - F1F2

Step 3: Use the given information

We know that the resultant force is perpendicular to F1, which means that the angle between R and F1 is 90 degrees. Therefore, we can use the Pythagorean theorem to get:

R² = F1² + F2²

Substituting R = 10, we get:

100 = F1² + F2²

Step 4: Solve for F1

We now have two equations for F1 and F2:

100 = F1² + F2²
100 = F1² + F2² - F1F2

Subtracting the second equation from the first, we get:

0 = F1F2

Since F2 cannot be zero (otherwise there would be no angle between the forces), we have:

F1 = 0

Therefore, one of the forces is zero.

Answer: One of the forces is zero.

Tan 30 degree =1/root3=x/10