The Question is from neet-chemistry atomic-structure parallelogram-law-of-vectors, and it was created by the author Mr. S M HUSSAIN

Question

Two forces of magnitudes 5 N and 7 N act on a particle at an angle of 60 degrees. According to the parallelogram law, what is the magnitude of the resultant force?

Mr. S M HUSSAIN · Accepted Answer

## CORE INFORMATION
✓ **Answer**: C
## CONCEPT FRAMEWORK
 **Primary Concept**: Parallelogram Law of Vector Addition
 **Related Topics**: Resultant force, vector magnitudes, trigonometry
 **Prerequisites**: Understanding of vectors, trigonometric functions (cosine rule)
## SOLUTION PATHWAY
**Given Information**:
  Force 1 ($F_1$) = 5 N
  Force 2 ($F_2$) = 7 N
  Angle between forces ($	heta$) = 60 degrees
**Method & Steps**:
 1. Apply the parallelogram law of vector addition to find the magnitude of the resultant force ($R$).  The parallelogram law states that the square of the resultant force is equal to the sum of the squares of the individual forces plus twice the product of the magnitudes of the forces and the cosine of the angle between them.
  Reasoning: This law allows us to determine the magnitude of the resultant force when two forces act at an angle.
  Formula/Rule: $R^2 = F_1^2 + F_2^2 + 2F_1F_2cos(	heta)$
 2. Substitute the given values into the formula:
  Working: $R^2 = 5^2 + 7^2 + 2(5)(7)cos(60°)$ 
                $R^2 = 25 + 49 + 70(0.5)$
                $R^2 = 25 + 49 + 35$
                $R^2 = 109$
                $R = \sqrt{109} \approx 10.44 N$
  Key Point: Remember to use the cosine of the angle between the forces.
 3. Calculate the magnitude of the resultant force.
  Result: 10.44 N
  Verification: Check the calculation and units.
 ## OPTION ANALYSIS
A :x: 12 N: This value is significantly higher than the expected magnitude.
B :x: 2 N: This value is too low; it would only be possible if the forces were almost directly opposing each other.
C ✓: 10.44 N: This value is consistent with the parallelogram law calculation.
D :x: 8.6 N: This value is close but still incorrect due to rounding errors or miscalculation in applying the parallelogram law.
 ## LEARNING AIDS
 **Common Mistakes**:
  1.Incorrectly applying the parallelogram law formula (e.g., forgetting the $2F_1F_2cos(	heta)$ term or using the wrong trigonometric function).
  2.Using the incorrect angle in the cosine function. Ensure the angle used is the angle between the two vectors.
 **Quick Tips**:
  1.Draw a vector diagram to visualize the forces and their resultant before applying the formula. This helps avoid errors in interpretation.
  2.Remember the parallelogram law formula: $R^2 = F_1^2 + F_2^2 + 2F_1F_2cos(	heta)$

Mr. S M HUSSAIN · Answer

12 N

Mr. S M HUSSAIN · Answer

2 N

Mr. S M HUSSAIN · Answer

The correct Option is "10.44 N"

Mr. S M HUSSAIN · Answer

8.6 N

NEET Chemistry Structure Of Atom Parallelogram Law Of Vectors MCQs

Select Topic

Question Tags

Question Tags

Question Tags

Question Tags

Question Tags

Question Tags

Question Tags

Question Tags

Question Tags

Question Tags

NEET Subjects

Our Bots

Company