Question

A block of mass m moving with velocity $v_0$ on a smooth horizontal surface hits the spring of constant k as shown.The maxi um compression in spring is

• A. $\sqrt{\frac{2m}{k}}.v_0$
• B. $\sqrt{\frac{m}{k}}.v_0$
• C. $\sqrt{\frac{m}{2k}}.v_0$
• D. $\frac{2m}{k}.v_0$

Answer 1

The correct option is B $\sqrt{\frac{m}{k}}.v_0$

For maximum compression,the kinetic energy of the blcok gets converted to the potential energy of the spring:

$\frac{1}{2}m{v}_0^2=\frac{1}{2}k{x}^2$

$x^2=\frac{m{v}_0^2}{k}$

$x=\sqrt{\frac{m}{k}}.v_0$