Question

Two forces one 6 newton and the other of 8 newton act on a point at right angles to each other. The resultant of these forces is (in newton)

Answer 1

Using parallelogram law
R = √ P^2 + Q^2 + 2PQ CosΦ
where
R = Resultant Of the
P, Q = Magnitude of vector P and Q
Φ= Angle between two Vector

Then Substituting the values we get

R = √ 6^2 + 8^2 + 2*6*8 Cos 90
= √36+64 + 96*0
= √ 100
= 10N

So, The Resultant of these forces is 10N.

Answer 2

The resultant of the forces is 10 N

• Force is a vector quantity, as it has both magnitude and direction, and it follows the vector rule of addition.
• So, the resultant of the forces will also be calculated by the rule of vector addition.

We know, if A and B are two vectors and the angle between them is θ, the resultant between them will be,

R = (A² + B² + 2AB Cosθ)$^{1/2}$

Given,

The two forces are = 6 N and 8 N

The angle between them is = 90°

∴ R = (6² + 8² + 2×6×8 Cos 90°)$^{1/2$

⇒ R = (36 + 64)$^{1/2$ [As Cos 90° = 0]

⇒ R = √100

⇒ R = 10

∴ The resultant force is 10 N.