A body is in equilibrium under three concurrent forces. If two forces are perpendicular, the third force must be:
A. Equal to sum of the two
B. Equal to vector sum of the two
C. Zero
D. Equal and opposite to vector sum of the two
Answer: Option D
Solution (By JKSSB Mock Tests)
For equilibrium, net force = 0. If forces F₁ and F₂ are perpendicular, their vector sum R = √(F₁² + F₂²). The third force F₃ must balance R, so F₃ = -R, i.e., equal in magnitude and opposite in direction to the vector sum of F₁ and F₂. Memory aid: 'Equilibrium: vector sum of all forces = 0; third force closes the triangle'. This statics concept is frequently tested in competitive exams. Always use vector addition for force equilibrium; scalar sum is incorrect for non-collinear forces.
Explanation:
KE ∝ p². Double KE ⇒ p_new = √2 p_old ⇒ increase = (√2 - 1)×100% ≈ 41.4%. Memory tip: 'KE ∝ p²; %Δp ≈ ½ %ΔKE for small changes, but use exact for large'. Energy-momentum relation frequently tested in competitive exams.
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