Question

A block of mass $m$ moving with a velocity $v_0$ on a smooth horizontal floor collides with a light spring of stiffness $k$ that a rigidly fixed horizontally with a vertical wall. If the maximum force imparted by the spring on the block is $F$, then

• A. $F\propto \sqrt{m}$
• B. $F\propto \sqrt{k}$
• C. $F\propto v_0$
• D. None of these

Answer 1

Answer: (A), (B), (C)

The correct options are
A $F\propto \sqrt{m}$
B $F\propto \sqrt{k}$
C $F\propto v_0$

Energy conservation between the position A and B
$\Delta PE=\Delta KE=0\Rightarrow \frac{1}{2}m{x}^2-\frac{1}{2}m{v}_0^2=0\Rightarrow x=\sqrt{\frac{m}{k}}{v}_0$
$\therefore F_{max}=kx=\sqrt{km{v}_0}\Rightarrow F_{max}\propto \sqrt{k}$
$\propto \sqrt{m}$
$\propto \sqrt{v_0}$