IIT-JEE 2008 · Paper 2 · Physics Q26

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PhysicsSingle correct+3 / -1Question 26 of 66

A block (B) is attached to two unstretched springs S1 and S2 with spring constants $k$ and $4k$ , respectively (see figure I). The other ends are attached to identical supports M1 and M2 not attached to the walls. The springs and supports have negligible mass. There is no friction anywhere. The block B is displaced towards wall 1 by a small distance $x$ (figure II) and released. The block returns and moves a maximum distance $y$ towards wall 2. Displacements $x$ and $y$ are measured with respect to the equilibrium position of the block B. The ratio $\frac yx$ is

Figure I: between wall 2 (left) and wall 1 (right), block B joined by spring S2 (4k) to support M2 at wall 2 and by spring S1 (k) to support M1 at wall 1; supports rest against the walls but are not attached. Figure II: B displaced a distance x towards wall 1; M2 has moved a distance x away from wall 2.

\frac12

\frac14

Answer and worked solution

Official answer: C

Towards wall 1. S1 (k) is compressed against M1 and wall 1. S2 would be stretched, but M2 is not fixed, so it simply follows (no tension). Stored energy: $\frac12kx^2$ .

Towards wall 2. Now S2 (4k) is compressed against M2 and wall 2, while S1 goes slack (M1 leaves wall 1). The block stops when
$\frac12kx^2=\frac12(4k)y^2\implies\frac yx=\frac12.$

(C)

Topics:Spring-mass systems Spring potential energy

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IIT-JEE 2008 · Paper 2, Physics question 26