Question

Two forces of 4 N and 3 N are acting on body in perpendicular. The resultant of these forces is (a) 7 N (b) 5 N (c) 1 N (d) 2 N

Answer 1

Answer:

b 5N

Explanation:

As they are perpendicular, The angle between them is 90⁰

We know the formula

R=

$\sqrt{x {}^{2} + y {}^{2} + 2xy \cos(theta) }$

where theta is 90⁰, Thus the value of 2xycos(theta) is 0.

Now, x=3N and y= 4N.

after substituting values, the answer we get is 5N.

Answer 2

Question :

Two forces of 4 N and 3 N are acting on body in perpendicular. The resultant of these forces is (a) 7 N (b) 5 N (c) 1 N (d) 2 N

Given :

• Two forces of 4N and 3N are acting on body in perpendicular.

To find :

• Resultant of these forces

Solution :

Resultant of these forces can be found in 2 ways.

Number 1 way is through pythagoras theorem as they are acting in perpendicular :

⇒ Resultant (c)² = a² + b²

Where,

• a = 4 N
• b = 3 N

⇒ Resultant force² = 4² + 3²

⇒ Resultant force² = 16 + 9

⇒ Resultant force² = 25

⇒ Resultant force = √25

⇒ Resultant force = 5 N

∴ Resultant of these forces is = b) 5 N

Number 2 way :

Resultant of forces is given by,

⇒ Resultant force, R = √(a² + b² + 2abcosθ

• Here, θ = 90°

⇒ R = √(4² + 3² + 2ab cos90°)

• cos90° = 0

⇒ R = √(16 + 9 + 2ab × 0)

⇒ R = √(25 + 0)

⇒ R = √25

⇒ R = 5 N

∴ Option (b) is correct : 5 N