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Question

# A block (B) is attached to two unstretched springs S1 and S2 with spring constant 2k and 4k respectively. The other ends are attached to two supports m1 and m2 not attached to the walls. The springs and supports have negligible mass and the surface is frictionless. The block B is displaced towards wall 1 by a small distance x and released. The block returns and moves a maximum distance y towards wall 2. Displacement x and y is measured with respect to the equilibrium position of the block B. The ratio of yx is

A
12
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B
2
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C
2
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D
12
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Solution

## The correct option is D 1√2Given that, Spring constant of spring S1=2k Spring constant of spring S2=4k Initial compression of spring S1=x Energy stored in spring S1=12×2kx2 =kx2 ……(i) The block will return from wall 1 and moves toward wall 2 and spring S2 will be compressed. Energy stored in S2=124ky2=2ky2 By energy conservation, Energy stored in spring S1 initially = Energy stored in S2 finally ⇒kx2=2ky2 ⇒x2y2=21 ⇒yx=1√2

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