Question

Resultant of two froce 3N nad 4N acting ar apoit is 5N show that the two froce are 2 perpendicular to each other

Answer 1

Given:

• Two forces, A = 3N and B = 4N
• Resultant of these forces, R = 5N

To prove:

• Two forces are perpendicular to each other.

Knowledge required:

• Formula to calculate magnitude of resultant 'R' of two forces 'A' and 'B' when they are at an angle 'p' to each other.

R² = A² + B² + 2 AB cos p

Proof:

Let, the angle between A and B be 'p', then the resultant R will be,

➡ R² = A² + B² + 2 AB cos p

[ putting values ]

➡ (5)² = (3)² + (4)² + 2 (3) (4) cos p

➡ 25 = 9 + 16 + 24 cos p

➡ 25 = 25 + 24 cos p

➡ 25 - 25 = 24 cos p

➡ 0 = 24 cos p

➡ cos p = 0

[ since, cos 90° = 0 ]

➡ cos p = cos 90°

➡ p = 90°

Hence, Proved that

• Forces A = 3N and B = 4N are Perpendicular to each other.