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Physics-

General

Easy

Question

A block(B) is attached to two unstretched springs $S subscript 1 end subscript a n d blank S subscript 2 end subscript$ with springs constants $k blank a n d blank 4 k comma$ representively (see Fig. I) The other ends are attached to identical supports $M subscript 1 end subscript$ and $M subscript 2 end subscript$ not attached to the walls. The springs and supports have negligible mass. There is no friction anywhere. The block $B$ is displaced towards wall I by small distance $x left parenthesis F i g blank I I right parenthesis$ and released. The block returns and moves a maximum distance y towards wall 2.Displacements $x blank a n d blank y$ are measured with respect to the equilibrium position of the block $B$ The ratio $fraction numerator y over denominator x end fraction$ is

4
2
$\frac{1}{2}$
$\frac{1}{4}$

The correct answer is: $fraction numerator 1 over denominator 2 end fraction$

From energy conservation,
$fraction numerator 1 over denominator 2 end fraction k x to the power of 2 end exponent equals fraction numerator 1 over denominator 2 end fraction open parentheses 4 k close parentheses y to the power of 2 end exponent$
$fraction numerator y over denominator x end fraction equals fraction numerator 1 over denominator 2 end fraction$

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