Question

A block of mass 'm' resting on a smooth horizontal floor is attached to a spring of force constant 'K' whose other end is attached to a rigid wall as shown in the figure above. A second block of mass 'm' is projected directly towards the first block with a velocity 'u'. After a collision, the two blocks stick together. The maximum compression in the spring is

• A. $\sqrt{\frac{m{u}^2}{K}}$
• B. $\sqrt{\frac{2m{u}^2}{K}}$
• C. $\sqrt{\frac{m{u}^2}{2K}}$
• D. $\sqrt{\frac{m{u}^2}{4K}}$

Answer 1

Answer: (C)

$\sqrt{\frac{m{u}^2}{2K}}$

Its an example of inelastic collision so, energy is not conserved all the time.
Momentum conservation is applicable.
$mu=2mv$
$\Rightarrow v=\frac{u}{2}$

Now after the collision, we can apply energy conservation.

Maximum compression when kinetic energy is zero.
$\frac{1}{2}\left(2m\right)\frac{u^2}{4}=\frac{1}{2}K{x}^2$

$x=\sqrt{\frac{m{u}^2}{2K}}$