As shown in the figure, an iron block A of volume 0 . 25 m 3 is attached to a spring S of unstretched length 1 . 0 m and hanging to the ceiling of a roof. The spring gets stretched by 0 . 2 m . This block is removed and another block B of iron of volume 0 . 75 m 3 is now attached to the same spring and kept on a frictionless incline plane of 30 ° inclination. The distance of the block from the top along the incline at equilibrium is

Question

As shown in the figure, an iron block A of volume 0 . 25 m 3 is attached to a spring S of unstretched length 1 . 0 m and hanging to the ceiling of a roof. The spring gets stretched by 0 . 2 m . This block is removed and another block B of iron of volume 0 . 75 m 3 is now attached to the same spring and kept on a frictionless incline plane of 30 ° inclination. The distance of the block from the top along the incline at equilibrium is, 1 . 1 m, 1 . 3 m, 1 . 6 m, 1 . 9 m

MARKS App · Accepted Answer

The free body diagrams of the blocks are shown in the figure below. At equilibrium, the net force on a body is zero. Therefore, For block A , m A g = k x ⇒ k = m A g x And for block B , m B g sin 30 ° = k x ' ⇒ x ' = m B g 2 m A g x Since the same material is used for both the blocks, their masses will be proportional to their volume. ⇒ x ' = V B 2 V A x = 0 . 75 2 × 0 . 25 × 0 . 2 = 0 . 3 m . Therefore, the distance of block B from the top is d = l + x ' = 1 . 3 m .

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