### JEE Mains Previous Years Questions with Solutions

4.5
star star star star star
1

### AIEEE 2002

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
$4$ $cm$

## Explanation

We know the work energy theorem, $W = \Delta K = FS$

For first penetration, by applying work energy theorem we get,

${1 \over 2}m{v^2} - {1 \over 2}m{\left( {{v \over 2}} \right)^2} = F \times 3\,\,...(i)$

For second penetration, by applying work energy theorem we get,

${1 \over 2}m{\left( {{v \over 2}} \right)^2} - 0 = F \times S\,...(ii)$

On dividing $(ii)$ by $(i)$

${{1/4} \over {3/4}} = S/3$

$\therefore$ $S = 1\,cm$