question_answer

If a body loses half of its velocity on penetrating 3cm in a wooden block, how much will it penetrate more before coming to rest?

A)  1 cm

B)  2 cm

C)  3 cm                     

D)  4 cm

Correct Answer: A

Solution :

   \[{{v}^{2}}-u_{2}^{{}}=2as(or){{v}^{2}}-{{u}^{2}}\propto S\] \[\frac{{{S}_{2}}}{{{S}_{1}}}=\frac{V_{2}^{2}-u_{2}^{2}}{v_{1}^{2}-u_{1}^{2}}\]                  \[\frac{{{S}_{2}}}{3}=\frac{{{0}^{2}}-{{\left( \frac{v}{2} \right)}^{2}}}{{{\left( \frac{v}{2} \right)}^{2}}-{{V}^{2}}}\,\,\frac{{{S}_{2}}}{3}=\frac{-\frac{{{V}^{2}}}{4}}{\frac{3{{v}^{2}}}{4}}\]              \[\Rightarrow {{S}_{2}}=1=1cm\]