Two bodies $A$ and $B$ of mass $m$ and $2\, m$ respectively are placed on a smooth floor. They are connected by a spring of negligible mass. $A$ third body $C$ of mass $m$ is placed on the floor. The body $C$ moves with a velocity $v_0$ along the line joining $A$ and $B$ and collides elastically with $A$. At a certain time after the collision it is found that the instantaneous velocities of $A$ and $B$ are same and the compression of the spring is $x_0$. The spring constant $k$ will be
Two bodies $A$ and $B$ of mass $m$ and $2\, m$ respectively are placed on a smooth floor. They are connected by a spring of negligible mass. $A$ third body $C$ of mass $m$ is placed on the floor. The body $C$ moves with a velocity $v_0$ along the line joining $A$ and $B$ and collides elastically with $A$. At a certain time after the collision it is found that the instantaneous velocities of $A$ and $B$ are same and the compression of the spring is $x_0$. The spring constant $k$ will be
- [AIEEE 2012]
- A
$m\,\frac{{v_0^2}}{{x_0^2}}$
- B
$m\,\frac{{{v_0}}}{{2{x_0}}}$
- C
$2m\,\frac{{{v_0}}}{{{x_0}}}$
- D
$\frac{2}{3}m\,{\left( {\frac{{{v_0}}}{{{x_0}}}} \right)^2}$
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