JEE Advanced · 2008 · 13 Apr 2008 · Paper 2 · Elasticity & SHM

A block (B) is attached to two unstretched springs S1 and S2 with spring constants

k

and

4 k

, 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{y}{x}

(A)4
(B)2
(C) $\frac{1}{2}$ ✓ Correct
(D) $\frac{1}{4}$

Answer: (C)

Solution

When the block is displaced by distance

x

towards wall 1, spring S1 (constant

k

) is compressed and stores energy

\frac{1}{2} k x^{2}

.

When the block moves maximum distance

y

towards wall 2, spring S2 (constant

4 k

) is compressed and stores energy

\frac{1}{2} (4 k) y^{2}

.

By energy conservation:

\frac{1}{2} k x^{2} = \frac{1}{2} (4 k) y^{2}

x^{2} = 4 y^{2}

\frac{y}{x} = \frac{1}{2}

JEE Advanced · 2008 · 13 Apr 2008 · Paper 2 · Single correct option

Practise more: all JEE Advanced PYQs on Elasticity & SHM →

JEE Advanced · 2008 · 13 Apr 2008 · Paper 2 · Elasticity & SHM

Solution

More JEE Advanced questions on Elasticity & SHM