question_answer

If a body looses half of its velocity on penetrating 3 cm in a wooden block, then 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 :

 

Case (i)	Case (ii)
\[{{u}_{1}}=u\]	\[{{u}_{2}}=u-2\]
\[{{v}_{1}}=\frac{u}{2}\]	\[=\frac{u}{2}\]
\[{{a}_{1}}=-a\]	\[{{a}_{2}}=-a\]
\[{{S}_{1}}=3\,cm\]	\[{{S}_{2}}=?\]
\[\frac{{{u}^{2}}}{4}-{{u}^{2}}\]	\[{{O}_{2}}-\frac{{{u}^{2}}}{4}=2\times (-a)\times {{S}_{2}}\]
	\[=2\times (-a)\times 3\]
\[-\frac{3}{4}{{u}^{2}}=-6a\]	\[-\frac{{{u}^{2}}}{4}=-2a{{s}_{2}}\]
\[\frac{3{{u}^{2}}}{4}=6a\]……(1)	\[\frac{{{u}^{2}}}{4}=2a{{s}_{2}}\]…..(2)
\[\frac{\frac{{{u}^{2}}}{4}}{\frac{3{{u}^{2}}}{4}}=\frac{2a{{s}_{2}}}{6a}\]	\[\frac{1}{3}=\frac{1}{3}{{S}_{2}}\]
\[{{S}_{2}}=1\,cm\]