question_answer

    If a body loses half of its velocity on penetrating 3cm 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 :

                Let initial velocity of body at point A is v, AB is 3 cm. From                     \[{{v}^{2}}={{u}^{2}}-2as\]                 \[{{\left( \frac{v}{2} \right)}^{2}}={{v}^{2}}-2a\times 3\]                 \[a=\frac{{{v}^{2}}}{8}\] Let on penetrating 3 cm in a wooden block, the body moves x distance from B to C. So, for B to C                 \[u=\frac{v}{2},v=0,\] \[s=x,a=\frac{{{v}^{2}}}{8}\]             (deceleration) \[\therefore \]  \[{{(0)}^{2}}={{\left( \frac{v}{2} \right)}^{2}}-2.\frac{{{v}^{2}}}{8}.x\]                 \[x=1\]