Q.
A block(B) is attached to two unstretched springs $S_{1}and\ S_{2}$ with springs constants $k\ and\ 4k,$representively (see Fig. I)The other ends are attached to identical supports $M_{1}$ and $M_{2}$ 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 $x(Fig\ II)$ 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 $\frac{y}{x}$ is
A) 4
B) 2
C) $\frac{1}{2}$
D) $\frac{1}{4}$
Explanation
(c) From energy conservation,
$\frac{1}{2}kx^{2} = \frac{1}{2}(4k)y^{2}$
$\frac{y}{x} = \frac{1}{2}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.