A bullet is fired normally on an immovable wooden plank. It loses 25% of its momentum in penetrating a thickness of 3.5cm. The total thickness penetrated by the bullet is

Let $ucm{s}^{-1}$ be the speed of the bullet. Since the mass of the bullet remains unchanged, its speed becomes $\upsilon =\frac{3u}{4}cm{s}^{-1}$ after it penetrates a distance x = 3.5 cm. The retardation a due to the resistance of the wooden is given be $u^2-{\upsilon }^2=2ax$ or $u^2-{\left(\frac{3u}{4}\right)}^2=2a\times 3.5$

Which gives $a=\frac{u^2}{16}cm{s}^{-2}.$ The bullet will come to rest when its velocity $\upsilon \text{'}=0.$ If $x\text{'}$ is the thickness penetrated by the bullet, then $u^2-\upsilon {\text{'}}^2=2ax\text{'}$ or $x\text{'}=\frac{u^2}{2a}$ but $a=\frac{u^2}{16}cm{s}^{-2}.$

Therefore  $x\text{'}=\frac{u^2\times 16}{2u^2}=8cm$

Hence the correct choice is (a)