Question 106 of 130

Blocks of masses $\text{m}, 2\text{m}, 4\text{m}$ and $8\text{m}$ are arranged in a line of a frictionless floor. Another block of mass $m$ , moving with speed $υ$ along the same line (see figure) collides with mass $m$ in perfectly inelastic manner. All the subsequent collisions are also perfectly inelastic. By the time the last block of mass $8\text{m}$ starts moving the total energy loss is \text{p%} of the original energy. Value of ‘$\text{p}$ ’ is close to:

A$77$B$94$C$37$D$87$

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Answer: (B) $94$

Inelastic collision
$mv=16 {mv}^{1}$
$\Delta K loss=\dfrac{1}{2}{mv}^{2}-\dfrac{1}{2}\left(16M\right){\left(\dfrac{v}{16}\right)}^{2}$
$=\dfrac{1}{2}{mv}^{2}-\dfrac{1}{2}M\dfrac{{v}^{2}}{16}$
$=\dfrac{1}{2}{mv}^{2}\left(\dfrac{15}{16}\right)$
$$