Question

A block C of mass m is moving with velocity $v_0$ and collides elastically with block A of mass m which is connected to another block B of mass $2$m through a spring of spring constant k. What is k if $x_0$ is the compression of spring when velocity of A and B is same?

• A. $\frac{m{v}_0^2}{x_0^2}$
• B. $\frac{m{v}_0^2}{2x_0^2}$
• C. $\frac{3}{2}\frac{m{v}_0^2}{x_0^2}$
• D. $\frac{2}{3}\frac{m{v}_0^2}{x_0^2}$

Answer 1

The correct option is D $\frac{2}{3}\frac{m{v}_0^2}{x_0^2}$

After collision $V_c=0$

By momentom conservation,

$m{v}_0=(m+2m)uu=\frac{1}{3}{v}_0$

Applying energy conservatioln,

$\frac{1}{2}m{v_0}^2=\frac{1}{2}(m+2m)u^2+\frac{1}{2}k{x_0}^2\frac{1}{2}(m{v_0}^2-\frac{{m{v}_0}^2}{3})=\frac{1}{2}k{x_0}^{2}k=\frac{2m{v_0}^2}{3{x_0}^2}$