As shown in the following figures, block of mass 2 k g is in equilibrium in the vertical plane. At a certain instant right spring in case- 1 and right string in case- 2 are cut. Then the ratio of instantaneous acceleration of block in case- 1 to case- 2 just after the cutting is (strings and springs are ideal)

Step-by-step solution

2 Tsin ⁡ 37 ° = 20 2 T × 3 5 = 20 T = 50 3   N Now when spring is cut in case- 1 then net force F 1 acting on block is, F 1 = 20 2 + 50 3 2 - 2 × 20 × 50 3 × 3 5 (resultant force of the remaining T = 50 3   N and mg = 20   N forces) = 50 3   N Similarly, when the string is cut in case- 2 then net force F 2 acting on block is F 2 = 20 × 4 5 = 16   N ∴ a 1 a 2 = 50 3 × 1 16 = 50 48 = 25 24