Published by:
CGP EDU Academic Team
Published on: September 12, 2026
Two forces 
and 
lie in 
plane. The magnitudes and the angles of these forces with the 
-axis are 
Find their resultant.
Text Solution
Verified by ExpertsThe correct answer is:
C
Given two forces, F1 and F2, with their magnitudes and angles:
To find the resultant R, we use the component method:
Rx = F1cos(θ1) + F2cos(θ2) and Ry = F1sin(θ1) + F2sin(θ2)
Calculating the components:
Resultant magnitude R = \sqrt{Rx^2 + Ry^2}
Hence,
R = \sqrt{0^2 + (100\sqrt{2})^2} = 100\sqrt{2} N ≈ 141.42 N
Therefore, the correct option is C.
- F1 = 100 N, θ1 = 45°
- F2 = 100 N, θ2 = 135°
To find the resultant R, we use the component method:
Rx = F1cos(θ1) + F2cos(θ2) and Ry = F1sin(θ1) + F2sin(θ2)
Calculating the components:
- Rx = 100cos(45°) + 100cos(135°) = 100 × (\frac{\sqrt{2}}{2}) + 100 × (\frac{-\sqrt{2}}{2}) = 0
- Ry = 100sin(45°) + 100sin(135°) = 100 × (\frac{\sqrt{2}}{2}) + 100 × (\frac{\sqrt{2}}{2}) = 100\sqrt{2}
Resultant magnitude R = \sqrt{Rx^2 + Ry^2}
Hence,
R = \sqrt{0^2 + (100\sqrt{2})^2} = 100\sqrt{2} N ≈ 141.42 N
Therefore, the correct option is C.
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