Q132 / 160 · AP EAMCET 2022 (04 Jul Shift 2) · Physics

As shown in the figure, an iron block A of volume 0.25 m3 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 m3 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

Figure

  • A
    1.1 m
  • Correct answer
    B
    1.3 m
  • C
    1.6 m
  • D
    1.9 m

Solution

The free body diagrams of the blocks are shown in the figure below.

Figure

At equilibrium, the net force on a body is zero. Therefore,

For block A,

mAg=kx⇒k=mAgx

And for block B,

mBgsin30°=kx'⇒x'=mBg2mAgx

Since the same material is used for both the blocks, their masses will be proportional to their volume.

⇒x'=VB2VAx=0.752×0.25×0.2=0.3 m.

Therefore, the distance of block B from the top is d=l+x'=1.3 m.

Hence, the correct answer is option: 'B'.

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