Two forces having magnitude A and A/2 are perpendicular to each other. The magnitude of their resultant is:

Solution

Physics sir · 3 steps

Perpendicular forces form the two legs of a right triangle, so the resultant is just Pythagoras.

1. Angle is 90°. The general resultant is R = √(P² + Q² + 2PQ cos θ). For perpendicular forces θ = 90° and cos 90° = 0, so the cross term drops out.

   R = √(A² + (A/2)²) = √(A² + A²/4) = √(5A²/4)

2. Take the root. √(5A²/4) = (√5 A)/√4 = (√5 A)/2. The root acts on the 4 in the denominator as well, giving 2.
3. So. The resultant has magnitude √5A/2, which is option (c).

The idea to keep. For two perpendicular vectors, add their squares and take the square root. Do the root on numerator and denominator both, and check the units come out as a force.

Answer from the NTA final answer key. Solution by PrepWiser.