Question

In the figure shown here, the maximum compression in the ideal spring is (K is spring constant)

• A. $\sqrt{\frac{mv^{2}}{2K}}$
• B. $\sqrt{\frac{2mv^{2}}{3K}}$
• C. $\sqrt{\frac{3mv^{2}}{2K}}$
• D. $\sqrt{\frac{mv^{2}}{3K}}$

Answer 1

Answer: (B)

At maximum compression both blocks have same velocity. $P_f \,=\,P_i\, and\,K_f \,=\,K_i$
$2mv\, =\, 3mv′$
$v'\,=\,\frac{2}{3}V$
$\frac{1}{2}(2m)v^2-\frac{1}{2}(3m)\frac{4v^2}{9}=\frac{1}{2}Kx^2$
$x = \sqrt{\frac{2mv^{2}}{3K}}$