A bullet is fired into a fixed target looses one third of its velocity after travelling \(4 \mathrm{~cm}\). It penetrates further \(\mathrm{D} \times 10^{-3} \mathrm{~m}\) before coming to rest. The value of \(D\) is:

\( \left(\frac{2 u}{3}\right)^2=u^2+2(-a)\left(4 \times 10^{-2}\right) \)

\( \frac{4 u^2}{9}=u^2-2 a\left(4 \times 10^{-2}\right) \)

\( -\frac{5 u^2}{9}=-2 a\left(4 \times 10^{-2}\right) \ldots(1) \)

\( 0=\left(\frac{2 u}{3}\right)^2+2(-a)(x) \)

\( -\frac{4 u^2}{9}=-2 a x \ldots(2) \)

\( (1) /(2) \)

\( \frac{5}{4}=\frac{4 \times 10^{-2}}{x} \)

\( x=\frac{16}{5} \times 10^{-2} \)

\( x=3 \cdot 2 \times 10^{-2} \mathrm{~m} \)

\( x=32 \times 10^{-3} \mathrm{~m}\)

Note : Since no option is matching, Question should be bonus.