question_answer

If a body loses half of its velocity on penetrating 3 cm in a wooden block, then how much will it penetrate more before coming to rest?                                                   [AIEEE 2002]

A) 1 cm

B) 2cm

C) 3 cm

D) 4 cm

Correct Answer: A

Solution :

[a] Let initial velocity of body at point A be v, AB is 3 cm.

From                 \[{{v}^{2}}={{u}^{2}}-2\]as

\[{{\left( \frac{v}{2} \right)}^{2}}={{v}^{2}}-2a\times 3\]

Let after penetrating 3 cm in a wooden block, the body moves x distance from B to C and comes to rest.

So, for B to C

\[u=\frac{v}{2},\,\,v=0\],

\[s=x,\,a=\frac{{{v}^{2}}}{8}\]           (retardation)

\[\therefore \]      \[{{(0)}^{2}}={{\left( \frac{V}{2} \right)}^{2}}-2.\frac{{{V}^{2}}}{8}.\,x\]

\[x=1\,cm\]

NOTE: Here, it is assumed that retardation is uniform.