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Consider a ball in equilibrium under three forces F1, F2, and F3. The following statements are given: (I) F1_vec + F2_vec = -F3_vec (II) F1² + F2² = F3² (III) If suddenly F3 is removed, instantaneous acceleration of the system is zero (IV) If force of gravity F3 is reversed in direction, the instantaneous acceleration of the system is upward. Which of the following physical situations satisfies condition (II)? List-I describes physical situations and List-II describes force assignments. Match condition (II) with all correct List-I entries. (P) Ball on two smooth surfaces: F1 = normal reaction of surface 1, F2 = normal reaction of surface 2 (Q) Ball suspended by two strings: F1 = tension in string 1, F2 = tension in string 2 (R) Block on surface with spring: F1 = normal reaction, F2 = spring force (S) Ball held by spring and string: F1 = spring force, F2 = string force (T) Block suspended by two strings: F1 = tension in string 1, F2 = tension in string 2
- (A) P, Q, T, U
- (B) P, Q, R, T
- (C) P, Q, S, T
- (D) P, R, T
Correct answer: (C) P, Q, S, T
Solution
Condition F1² + F2² = F3² means F1 perpendicular to F2 (since |F1+F2|² = F1² + F2² + 2F1.F2 = F3² requires F1.F2 = 0). Scenarios where the two supporting forces are perpendicular to each other satisfy this.
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